National Disaster Tax Relief Act of 2017 This bill amends the Internal Revenue Code to modify various tax deductions, credits, and requirements that affect disaster areas and U.S. possessions. With respect to areas in which a federally declared disaster occurred from 2012 through 2022, the bill allows: expensing of certain disaster expenses, modifications to rules regarding the deduction of losses attributable to disasters, additional new markets tax credits, an exclusion from gross income for certain cancellations of indebtedness, additional advance refundings of certain tax-exempt bonds, and additional low-income housing tax credit allocations. The bill permanently: (1) excludes from gross income disaster mitigation payments received from state and local governments, and (2) allows taxpayers to create tax-exempt catastrophe savings accounts to pay expenses related to a major disaster. With respect to U.S. possessions, the bill: repeals the limitation on the amount of distilled spirits excise taxes covered over (paid) to the treasuries of the Virgin Islands and Puerto Rico, makes permanent the tax deduction for income attributable to domestic production activities in Puerto Rico, modifies the rules for claiming the refundable portion of the child tax credit, and requires the Department of the Treasury to make payments to certain U.S. possessions to either compensate for revenue lost due to specified provisions in the bill or allow residents to benefit from the provisions.