<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2016-10-03</periodOfReport>

    <dateOfOriginalSubmission>2016-10-05</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000352363</issuerCik>
        <issuerName>Kate Spade &amp; Co</issuerName>
        <issuerTradingSymbol>KATE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001642932</rptOwnerCik>
            <rptOwnerName>Singer Jan</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O KATE SPADE &amp; COMPANY</rptOwnerStreet1>
            <rptOwnerStreet2>2 PARK AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10016</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-10-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>904</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $1 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>904</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>904</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This Form is being filed for purposes of reporting the Issuer's book-entry credit to Reporting Person of Phantom Stock pursuant to Reporting Person's election to defer receipt of cash compensation for Board and Board Committee retention and meeting fees under the Issuer's Outside Directors' Deferral Plan (the &quot;Plan&quot;). The amount of Phantom Stock credited equates to that number of whole shares of Common Stock at the closing price on 9/30/2016, which are equivalent in value to the cash fees otherwise payable to the Reporting Person as of the date recorded on Issuer's records.</footnote>
        <footnote id="F2">Pursuant to the Plan, participants may choose any month and year at least three years after the date of deferral for the distribution of the corresponding number of shares of Common Stock. The Phantom Stock is convertible to Common Stock on a one-for-one basis. If no date for distribution is chosen, the shares are distributed on the January 1 following the termination of the participant's membership on the Issuer's Board of Directors.</footnote>
        <footnote id="F3">The Form 4, as originally filed, incorrectly reported the number securities acquired. The Form 4, as amended by this Form 4/A, correctly reports such information.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Timothy F. Michno, as Attorney-in-Fact</signatureName>
        <signatureDate>2016-10-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
