Fred Mitchell was born in Rawdon, Yorkshire, England in 1863 and was articled to Charles D. Swale in Leeds, Yorkshire. He also attended Leeds Mechanics' Institute; and Leeds School of Art and School of Science in Leeds. He received additional training with with W. Hoffman Wood, a quantity surveyor, and William Wheater a civil engineer. He worked in the office of John Kirk (1817-1886), Albert Holmes Kirk (1840-1920), and James Sheard Kirk (1842-1911).
Mitchell commenced independent practice in Leeds in 1887 and was in partnership with Charles D. Swale as Swale & Mitchell. From 1897 he practised alone.
Mitchell's address was given as 8 Hessle Terrace, Bracewell, Yorkshire in 1911 and 1914; and 9, Upper Fountaine Street, Albion Street, Leeds in 1914. He died in Yorkshire in 1938. His death was registered in Leeds
Leeds Bowling Club Premises and Lodge; extensions, Burmantofts Conservative Club; now Leeds Constitutional Club; St. Oswald's Church Schools and Institute; All Souls' Church Recreation Hall; Bull and Bell Hotel, North Tavern; and numerous hotel alterations; clothing factory, Messrs. Camrass & Sons, Leeds; the Abbey Picture House, Kirkstall houses, Nottingham, Scarborough, Boston Spa, Rawdon, Horsforth, Leeds, &c.; Surveying and laying-out building estates — Scarborough, Horsforth, Collingham, Kirkstall, Leeds
Directory of British Architects 1834-1914. Compiled by Antonia Brodie, et al. Volume 2: L-Z. London; New York: British Architectural Library, Royal Institute of British Architects/Continuum, 2001