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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-06-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001722992</issuerCik>
        <issuerName>Spirit MTA REIT</issuerName>
        <issuerTradingSymbol>SMTA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001684096</rptOwnerCik>
            <rptOwnerName>Hsieh Jackson</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SPIRIT MTA REIT</rptOwnerStreet1>
            <rptOwnerStreet2>2727 NORTH HARWOOD STREET, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common shares of beneficial interest</value>
            </securityTitle>
            <transactionDate>
                <value>2018-06-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>61680</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>9.45</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>64271</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares sold to satisfy income tax withholding and remittance obligations of the reporting person arising from the pro rata distribution by Spirit Realty Capital, Inc. of shares of the Issuer on May 31, 2018 (the &quot;Spin-Off&quot;).</footnote>
        <footnote id="F2">The reporting person received an aggregate of 125,951 shares in the Spin-Off.</footnote>
    </footnotes>

    <remarks>Exhibit List: Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ Ricardo Rodriguez, Attorney-in-fact</signatureName>
        <signatureDate>2018-06-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
