Developing Alternative Mitigation Systems for Beavers Act or the DAMS for Beavers Act This bill directs the U.S. Fish and Wildlife Service (FWS) to establish a competitive grant program to assist projects that use nonlethal measures to reduce property damage caused by beavers and maintain or enhance habitat for beavers and other wildlife. In awarding grants, the FWS may prioritize projects that (1) include monitoring and research that facilitates evaluation of such projects and identification of best practices, (2) includes educational and outreach activities, (3) are located in an area that ensures grant recipients represent diverse geographic areas, and (4) satisfy any other criteria to effectively reduce damage to property and maintain or enhance habitat for beavers and other wildlife.