Safe American Food Exports Act of 2023 or the SAFE Act of 2023 This bill allows the Department of Agriculture (USDA) to preemptively negotiate regional export ban agreements for known animal disease threats that apply only to areas affected by animal disease outbreaks. These agreements enable the continuation of exports from areas not affected by an outbreak. The Animal and Plant Health Inspection Service, the Food Safety and Inspection Service (FSIS), and the Foreign Agricultural Service may negotiate the regionalization agreements with countries that have key export markets for any animal or article from the United States. In addition, USDA must promulgate a regulation requiring that, within three days of removing any language from the FSIS Import and Export Library, FSIS notify each state department of agriculture, each lead agency for animal disease, and any entity that petitioned for the inclusion of that language. (The FSIS library provides country and product specific information for (1) meat and poultry exports, and (2) products eligible for import to the United States.)