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 disaster mitigation and recovery expenses, (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, (3) exclude from gross income distributions from such accounts to pay disaster mitigation and recovery expenses; and (4) set forth tax rules and penalties for excess contributions to disaster savings accounts and for failure to file required reports on such accounts.