Service Dogs Assisting Veterans Act of 2025 or the SAVES Act of 2025This bill requires the Department of Veterans Affairs (VA) to establish a five-year pilot program to award grants on a competitive basis to nonprofit entities to provide service dogs to veterans who have certain disabilities, conditions, or diagnoses (e.g., a visual impairment).Under the program, the VA may provide up to $2 million to a nonprofit entity in a fiscal year.The VA must provide a veterinary insurance policy to veterans who receive a service dog through a grant under the program.