<?xml version="1.0" encoding="us-ascii"?>
<!-- DFIN ActiveDisclosure(SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date      : 2021-04-29T16:45:39.4850361+00:00 -->
<!-- Version            : 5.0.1.615 -->
<!-- Package ID         : 5a4b287570a64635b47d9d840788a4c2 -->
<!-- Copyright (c) 2021 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:element id="spsc_CurrentAmountRecognitionPeriodOfSetUpFees" name="CurrentAmountRecognitionPeriodOfSetUpFees" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_LongTermAmountRecognitionPeriodOfSetUpFees" name="LongTermAmountRecognitionPeriodOfSetUpFees" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_MaximumRecognitionPeriodForMiscellaneousOneTimeFee" name="MaximumRecognitionPeriodForMiscellaneousOneTimeFee" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="spsc_DeferredCostsIncurred" name="DeferredCostsIncurred" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_DeferredCostsAmortized" name="DeferredCostsAmortized" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_FinancialInstrumentsMaturitiesWithinOneYearFairValue" name="FinancialInstrumentsMaturitiesWithinOneYearFairValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_FinancialInstrumentsMaturitiesWithinOneToTwoYearFairValue" name="FinancialInstrumentsMaturitiesWithinOneToTwoYearFairValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_FinancialInstrumentAmortizedCostBasis" name="FinancialInstrumentAmortizedCostBasis" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="spsc_ScheduleOfFinancialInstrumentsLineItems" name="ScheduleOfFinancialInstrumentsLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_ScheduleOfFinancialInstrumentsTable" name="ScheduleOfFinancialInstrumentsTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_PPPLoanMember" name="PPPLoanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_FormerOwnersMember" name="FormerOwnersMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_ContingentConsiderationLiabilityMember" name="ContingentConsiderationLiabilityMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_OtherLeasesMember" name="OtherLeasesMember" type="nonnum: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_ScheduleOfStockholdersEquityLineItems" name="ScheduleOfStockholdersEquityLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_ScheduleOfStockholdersEquityTable" name="ScheduleOfStockholdersEquityTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_StockRepurchaseProgram1Member" name="StockRepurchaseProgram1Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_EmployeeStockPurchasePlanMember" name="EmployeeStockPurchasePlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_FourZeroOneKStockMatchMember" name="FourZeroOneKStockMatchMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <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_NetIncomePerShareAbstract" name="NetIncomePerShareAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="spsc_NumberOfJurisdictionOutsideUSHadExcessRevenueOfTenPercentage" name="NumberOfJurisdictionOutsideUSHadExcessRevenueOfTenPercentage" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
</xsd:schema>
