<?xml version="1.0" encoding="us-ascii"?>
<!-- DFIN ActiveDisclosure(SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date      : 2022-02-19T00:15:25.4907252+00:00 -->
<!-- Version            : 5.0.1.728 -->
<!-- Package ID         : c397b5b0e2954cf9b1d72f0e398783e8 -->
<!-- Copyright (c) 2022 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:element id="spsc_FiniteLivedIntangibleAssetsAccumulatedForeignCurrencyTranslationGainLoss" name="FiniteLivedIntangibleAssetsAccumulatedForeignCurrencyTranslationGainLoss" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_StockIssuedDuringPeriodSharesPursuantToStockAwards" name="StockIssuedDuringPeriodSharesPursuantToStockAwards" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_StockIssuedDuringPeriodValuePursuantToStockAwards" name="StockIssuedDuringPeriodValuePursuantToStockAwards" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="spsc_ReclassificationOfGainLossOnInvestmentsInToEarningsNetOfTax" name="ReclassificationOfGainLossOnInvestmentsInToEarningsNetOfTax" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="spsc_IncreaseDecreaseInOperatingLeases" name="IncreaseDecreaseInOperatingLeases" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_PaymentsToAcquireBusinessesAndIntangibleAssetsNetOfCashAcquired" name="PaymentsToAcquireBusinessesAndIntangibleAssetsNetOfCashAcquired" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="spsc_NonCashFinancingPaymentsProceedsFromPropertyAndEquipment" name="NonCashFinancingPaymentsProceedsFromPropertyAndEquipment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
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  <xsd:element id="spsc_GeographicInformationTextBlock" name="GeographicInformationTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_BusinessDescriptionPolicyPolicyTextBlock" name="BusinessDescriptionPolicyPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_InvestmentsPolicyTextBlock" name="InvestmentsPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_ScheduleOfEstimatedUsefulLifeOfPropertyAndEquipmentTableTextBlock" name="ScheduleOfEstimatedUsefulLifeOfPropertyAndEquipmentTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
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  <xsd:element id="spsc_DepreciationAndAmortizationExpenseOfPropertyAndEquipmentTableTextBlock" name="DepreciationAndAmortizationExpenseOfPropertyAndEquipmentTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_SummaryOfNonCancellableOperatingLeasesPrimarilyForOfficeSpaceTableTextBlock" name="SummaryOfNonCancellableOperatingLeasesPrimarilyForOfficeSpaceTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
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  <xsd:element id="spsc_BusinessCombinationDueToSellersRelatedWithinInitialNetWorkingCapitalAdjustment" name="BusinessCombinationDueToSellersRelatedWithinInitialNetWorkingCapitalAdjustment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
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  <xsd:element id="spsc_RecurringRevenuesTimingOfBillingsLatestPeriod" name="RecurringRevenuesTimingOfBillingsLatestPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_RecurringRevenuesTimingOfBillingsEarliestPeriodDescription" name="RecurringRevenuesTimingOfBillingsEarliestPeriodDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
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  <xsd:element id="spsc_RevenueRemainingPerformanceObligationForContractsOriginalDurations" name="RevenueRemainingPerformanceObligationForContractsOriginalDurations" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_EstimatedPeriodForMaterialRightsPresentToCustomers" name="EstimatedPeriodForMaterialRightsPresentToCustomers" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
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  <xsd:element id="spsc_MaximumRecognitionPeriodForMiscellaneousOneTimeFee" name="MaximumRecognitionPeriodForMiscellaneousOneTimeFee" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
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  <xsd:element id="spsc_InternallyDevelopedSoftwareMember" name="InternallyDevelopedSoftwareMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
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  <xsd:element id="spsc_LeaseExpirationDueDateYear" name="LeaseExpirationDueDateYear" type="dtr-types:gYearListItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_NumberOfOptionsToExtendLease" name="NumberOfOptionsToExtendLease" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_IncentivesReceivedUponExecutionOfAmendment" name="IncentivesReceivedUponExecutionOfAmendment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="spsc_CommitmentsAndContingenciesLineItems" name="CommitmentsAndContingenciesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
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  <xsd:element id="spsc_FifthAmendmentToLeaseAgreementRelatedToCurrentHeadquartersLocationMember" name="FifthAmendmentToLeaseAgreementRelatedToCurrentHeadquartersLocationMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_LeaseAgreementExpiresOnMayThirtyOneThousandTwentyFiveMember" name="LeaseAgreementExpiresOnMayThirtyOneThousandTwentyFiveMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract" name="CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_StockRepurchaseProgramEffectiveDate" name="StockRepurchaseProgramEffectiveDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_StockRepurchaseProgramUnusedAndExpiredShareRepurchaseAmount" name="StockRepurchaseProgramUnusedAndExpiredShareRepurchaseAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="spsc_TwoThousandAndSeventeenStockRepurchaseProgramMember" name="TwoThousandAndSeventeenStockRepurchaseProgramMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_TwoThousandAndNineteenStockRepurchaseProgramMember" name="TwoThousandAndNineteenStockRepurchaseProgramMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_TwoThousandAndTwentyOneStockRepurchaseProgramMember" name="TwoThousandAndTwentyOneStockRepurchaseProgramMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_StockRepurchaseProgram1Member" name="StockRepurchaseProgram1Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_PerformanceShareUnitsRestrictedStockUnitsAndDeferredStockUnitsMember" name="PerformanceShareUnitsRestrictedStockUnitsAndDeferredStockUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_RestrictedStockUnitsAndDeferredStockUnitsMember" name="RestrictedStockUnitsAndDeferredStockUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_EmployeeStockPurchasePlanMember" name="EmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_FourZeroOneKStockMatchMember" name="FourZeroOneKStockMatchMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfDelayedReceiptOfCommonShares" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfDelayedReceiptOfCommonShares" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndUnissuedInPeriod" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndUnissuedInPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_NumberOfOfferings" name="NumberOfOfferings" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="spsc_ShareBasedCompensationArrangementByShareBasedPaymentAwardValuePurchasedForAward" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardValuePurchasedForAward" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_EffectiveIncomeTaxRateReconciliationTaxBenefitsForExcessTaxDeductionFromStockActivity" name="EffectiveIncomeTaxRateReconciliationTaxBenefitsForExcessTaxDeductionFromStockActivity" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseForCompensation" name="EffectiveIncomeTaxRateReconciliationNondeductibleExpenseForCompensation" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_EffectiveIncomeTaxRateReconciliationForeignDerivedIntangibleIncome" name="EffectiveIncomeTaxRateReconciliationForeignDerivedIntangibleIncome" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_DeferredTaxAssetsOperatingLossAndTaxCreditCarryforwards" name="DeferredTaxAssetsOperatingLossAndTaxCreditCarryforwards" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_DeferredTaxAssetsOperatingLeaseLiabilities" name="DeferredTaxAssetsOperatingLeaseLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_DeferredTaxLiabilitiesDeferredRevenueAndExpense" name="DeferredTaxLiabilitiesDeferredRevenueAndExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="spsc_DeferredTaxLiabilitiesRightOfUseAssets" name="DeferredTaxLiabilitiesRightOfUseAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="spsc_DeferredTaxLiabilitiesPropertyPlantAndEquipmentAndOtherFiniteLivedAssets" name="DeferredTaxLiabilitiesPropertyPlantAndEquipmentAndOtherFiniteLivedAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="spsc_OperatingLossCarryforwardsExpirationDateOne" name="OperatingLossCarryforwardsExpirationDateOne" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_IncomeTaxExpenseBenefitLineItems" name="IncomeTaxExpenseBenefitLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_IncomeTaxExpenseBenefitTable" name="IncomeTaxExpenseBenefitTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_OperatingLossCarryforwardExpirableUnusedAmount" name="OperatingLossCarryforwardExpirableUnusedAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_TaxCreditCarryforwardBeginningExpirationYear" name="TaxCreditCarryforwardBeginningExpirationYear" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_TaxCreditCarryforwardEndingExpirationYear" name="TaxCreditCarryforwardEndingExpirationYear" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_NetIncomePerShareAbstract" name="NetIncomePerShareAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_DefinedContributionPlanEmployerNotNoteDiscretionaryContributionAmount" name="DefinedContributionPlanEmployerNotNoteDiscretionaryContributionAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_NumberOfJurisdictionOutsideUSHadExcessRevenueOfTenPercentage" name="NumberOfJurisdictionOutsideUSHadExcessRevenueOfTenPercentage" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_NonProfitOrganizationMember" name="NonProfitOrganizationMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
</xsd:schema>
