Corporal Alexander was a member of Company F, 2nd Battalion, 32nd Infantry Regiment, 7th Infantry Division. He was listed as Missing in Action while fighting the enemy on "Pork Chop Hill" in North Korea on 8 July 1953. He was presumed dead on 9 July 1954. His remains were not recovered. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Alexander was awarded the Purple Heart, the Combat Infantryman's Badge, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.