Small Business Paperwork Relief Act of 2013 - Amends the Paperwork Reduction Act to direct agency heads not to impose civil fines for first-time paperwork violations by small business concerns unless there is potential for serious harm to the public interest, the detection of criminal activity would be impaired, the violation is not corrected within six months, the violation is a violation of internal revenue law or a law concerning the assessment or collection of any tax, debt, revenue, or receipt, or the violation presents a danger to the public health or safety. Permits an agency to determine that a fine should not be imposed for a violation that presents a danger to public health or safety if the violation is corrected within 24 hours after receipt by the small business owner of notification of the violation.

Makes this Act inapplicable to any violation by a small business of a requirement regarding the collection of information by an agency if the small business previously violated any requirement concerning the collection of information by that agency.