Jumpstarting Our Business Sector Act of 2013 - Amends the Internal Revenue Code to: (1) eliminate the corporate income tax and the alternative minimum tax (AMT) on corporations in taxable years beginning after 2013; (2) exclude net capital gain from gross income; (3) extend for three years the increased depreciation allowance (bonus depreciation), the 100% expensing allowance for business assets, and the election to accelerate the AMT tax credit in lieu of bonus depreciation; and (4) repeal the estate, gift, and generation-skipping transfer taxes.