Safeguarding the U.S. Armed Forces and Service Academies Act This bill prohibits the use of federal funds to enforce or establish a mandate requiring a member of the Armed Forces, or a cadet or midshipman at a federal service academy, to receive a COVID-19 vaccination. Additionally, no such individuals may be subject to adverse action solely on the basis of a refusal to receive a COVID-19 vaccination. At the request of an individual who was involuntarily separated from an Armed Force or federal service academy solely because of a refusal to receive a COVID-19 vaccination, the military department concerned must reinstate the individual as a member of the Armed Force in the same rank and grade the individual held at the time of separation, or reinstate the individual as a cadet or midshipman with the credits the individual had completed at the time of separation; expunge from the individual's military service record any reference to adverse action related to the refusal to receive a COVID-19 vaccination; and include the period between the involuntary separation and reinstatement in the computation of retired or retainer pay of the individual. Such individuals must be entitled to back pay for the period between the separation and the reinstatement. The bill requires that the discharge of members due to the failure to obey a lawful order to receive a COVID-19 vaccination must be categorized as an honorable discharge, including for individuals who were discharged prior to the enactment of this bill.