Disaster Savings Accounts Act of 2013 - Amends the Internal Revenue Code to: (1) establish tax-exempt disaster savings accounts to pay the expenses of homeowners for equipment and materials for mitigating the effects of a natural disaster, (2) allow a deduction from gross income (above-the-line deduction) up to $5,000 (adjusted annually for inflation) in a taxable year for cash contributions to such accounts, and (3) set forth tax rules for account distributions and failure to report on disaster savings accounts.