Shipbuilder. Born in Aberdeen and educated at Ledingham's Academy there, he took an apprenticeship at Footdee Engineering Works. Despite long working hours, he also studied at the University of Aberdeen. He moved to Newcastle in 1842 and then London in 1844 to work in a drawing office. He returned to Tyneside and set up his own shipbuilding yard. This grew is size and reputation, building ships for Russia and, in 1862, Mitchell helped the Russians set up shipyards in St. Petersburg and received several honours from that country. His shipyard was merged with that of his friend Sir William Armstrong's to form the Armstrong Mitchell & Co., then Armstrong-Whitworth and eventually Vickers.
Mitchell was awarded an honorary degree by the University of Aberdeen. He died in Newcastle but endowed a graduation hall for the University of Aberdeen, built within Marischal College, known as the Mitchell Hall.