After private tutoring, Mitchell attended the University of Edinburgh, and completed his training in the office of Robert Rowand Anderson, where he was articled from 1878 to 1883.
Their first commission came in 1883, for the proprietor of The Scotsman newspaper, John Ritchie Findlay, whose home, 3 Rothesay Terrace, he remodelled.
[1] Another significant early commission from Findlay was for Well Court, a workers' housing development in Dean Village, Edinburgh, which he worked on between 1883 and 1886.
[3] Practising as Sydney Mitchell & Wilson, they were appointed by the Board of Lunacy in Scotland (due to Mitchell's fathers position as Director), with commissions for Craighouse in Edinburgh, the Crichton Royal Institution in Dumfries, Melrose Asylum, and the Royal Victoria Hospital in Edinburgh.
He was cousin to the Scottish businessman Sir George Arthur Mitchell and designed his house at 9 Lowther Terrace in Kelvinside in Glasgow.