Alexander was born in 1837 in Scotland and he served with the US Navy. Not much is known about his early life or even his death. We do know that his actions earned him the Medal of Honor. The citation reads:

On board the U.S.S. Colorado during the capture of the Korean forts, June 11, 1871. Fighting at the side of Lt. McKee during this action, McKenzie was struck by a sword and received a severe cut in the head from the blow.