Martin Reeves was born in Albemarle County, Virginia, around 1844 and worked as a laborer before the war. He enlisted in the Union army on April 20, 1864, near Washington, D.C. His enlistment records describe him as 5 feet, 4 inches tall, with black hair, brown eyes, and a brown complexion. Reeves enlisted for a period of three years and mustered into Company H of the 23rd USCT Infantry Regiment later that day. 

The 23rd USCT took part in several important missions for the Union army. Its first campaign took place along the James River in June 1864 under the overall command of General Benjamin Butler. The army then reassigned them to escort the wagon trains of the Army of the Potomac through the Wilderness. The regiment helped besiege Petersburg, Virginia, from June 16, 1864, until April 2, 1865. During the Bermuda Hundred Campaign outside of Richmond, Reeves deserted his regiment during a march. The army officially listed him as a deserter on November 26, 1864, and the details of his postwar life remain unknown.