Joseph had enlisted in the United States Army. Entered the service via Regular Military. Served during the Vietnam War. He began his tour on January 3, 1968. Spellman had the rank of Specialist Four. His military occupation or specialty was Infantry Indirect Fire Crewman. Service number assignment was 17751073. Attached to 25th Infantry Division, 1st Battalion, 27th Infantry, B Company.

During his service in the Vietnam War, Army Specialist Four Spellman experienced a traumatic event which ultimately resulted in loss of life on February 16, 1968. Recorded circumstances attributed to: Died through hostile action, burns.

Joseph Victor Spellman is buried or memorialized at Fort Logan National Cemetery, Denver, Denver County, Colorado. This is a National American Cemetery administered through the Department of Veteran's Affairs.
Joseph is honored on the Vietnam Veteran's Memorial in Washington DC. Name inscribed at VVM Wall, Panel 39e, Line 67.