Mitchell was born in Wilkinsburg, a suburb of Pittsburgh, Pennsylvania, in 1856. His parents, Henry Zehring Mitchell and Elizabeth Ann (Cannon) Mitchell, were both Pennsylvania natives. He moved with his parents as an infant to St. Cloud, Minnesota, in May 1857. His father operated a store in St. Cloud as a drygoods and clothing merchant and general agent. Mitchell's early education was in the schools of St. Cloud, Minnesota. He received his preparatory education at Ann Arbor High School.