Supporting At-risk Veterans in an Emergency Act or the SAVE Act This bill authorizes the Department of Veterans Affairs to reallocate specified grant funds to provide food to homeless veterans during a covered public health emergency. Additionally, the bill authorizes grant recipients to use per diem payments to provide food and basic supplies for homeless veterans and formerly homeless veterans who experienced homelessness during the one-year period ending on the date of enactment of this bill. A covered public health emergency is defined to include (1) a public health emergency under the Robert T. Stafford Disaster Relief and Emergency Assistance Act, or (2) an emergency with respect to COVID-19 (i.e., coronavirus disease 2019) declared by a governmental authority.