Stop the Spread of Invasive Mussels Act of 2023 This bill provides for activities to control invasive species on federal lands and waters. The Bureau of Land Management, Bureau of Reclamation, National Park Service, and Forest Service may inspect and decontaminate watercraft entering and leaving federal land and water located within a river basin that contains a Bureau of Reclamation water project. The Bureau of Reclamation must establish a grant program to conduct inspections and decontamination of watercraft in reservoirs operated and maintained by Reclamation, including to purchase, establish, operate, or maintain a watercraft inspection and decontamination station. In carrying out the grant program, Reclamation shall coordinate with (1) states with Reclamation projects, (2) affected Indian tribes, and (3) the Aquatic Nuisance Species Task Force.