America's Small Business Tax Relief Act of 2013 - Amends the Internal Revenue Code to make permanent: (1) the 100% exclusion from gross income of gain from the sale of certain small business stock, (2) carrybacks and alternative minimum tax rules relating to small business tax credits, (3) the reduction in the recognition period for the built-in gains from the sale of S corporation stock, (4) the increased limitation for the expensing of depreciable business assets, (5) the use of the percentage of completion accounting method for long-term contracts, (6) the increased tax deduction for business start-up expenditures, and (7) the allowance of a deduction for health insurance premiums in computing net earnings from self-employment income.