Red was raised in New Jersey by a father who was an engineer and loved music, and a mother who loved poetry. His first instruments were piano, alto saxophone, and clarinet. Although Cornell University awarded an engineering scholarship to Mitchell, by 1947 he was in the US Army playing bass. The next year he was in a jazz trio in New York City.
Mitchell became known for performing and/or recording with Mundell Lowe, Chubby Jackson, Charlie Ventura, Woody Herman, Red Norvo, Gerry Mulligan, and, after joining the West Coast jazz scene in the early 1950s, with Andre Previn, Shelly Manne, Hampton Hawes, Billie Holiday, Ornette Coleman, and others. He also worked as a bassist in the TV and film studios around Los Angeles, occasionally appearing on screen. Mitchell also appeared in documentaries about Tal Farlow, and Zoot Sims.
Saxophonist Harold Land and Mitchell founded and co-led a quintet in the early 1960s. In 1966, Red began tuning his bass in fifths (as the violin, viola, and cello are tuned), and his tuning method opened up many possibilities for bassists.
Mitchell moved to Stockholm in 1968 and he won Swedish Grammy Awards in 1986 and 1991 for his recorded performances as a pianist, bassist, and vocalist, and for his compositions and poetic song lyrics.
Mitchell se hizo conocido por actuar y / o grabar con Mundell Lowe, Chubby Jackson, Charlie Ventura, Woody Herman, Red Norvo, Gerry Mulligan y, luego de unirse a la escena del jazz de la Costa Oeste a principios de los años cincuenta, con Andre Previn, Shelly Manne, Hampton Hawes, Billie Holiday, Ornette Coleman, y otros. También trabajó como bajista en los estudios de televisión y cine de Los Ángeles, apareciendo ocasionalmente en la pantalla. Mitchell también apareció en documentales sobre Tal Farlow y Zoot Sims.
El saxofonista Harold Land y Mitchell fundaron y lideraron un quinteto a principios de los años sesenta. En 1966, Red comenzó a afinar su bajo en quintos (como el violín, la viola y el violonchelo están afinados), y su método de afinación abrió muchas posibilidades para los bajistas.
Mitchell se mudó a Estocolmo en 1968 y ganó los Premios Grammy de Suecia en 1986 y 1991 por sus actuaciones grabadas como pianista, bajista y vocalista, y por sus composiciones y letras de canciones poéticas.


















