Born in Dublin, Ireland, he served as a First Sergeant in Company I, 5th Infantry, US Army. While serving an escort for a expedition force at the Upper Washita, Texas, September 9, 1874, First Sergeant Mitchell's supply train was attacked by a large Indian war party. In the following days, he helped repel continuous fire and two major attacks by waves of Indians numbering more than 400 until the relief column arrived. For gallantry in action, he was awarded the Medal of Honor on April 23, 1875.