Mitchell was born and raised in Miami, Florida, United States. He began playing trumpet in high school, with the nickname "Blue".
After high school, he played in the rhythm & blues ensembles of Paul Williams, Earl Bostic, and Chuck Willis. He returned to Miami and was heard by Cannonball Adderley, with whom he recorded for Riverside Records in New York in 1958.
Mitchell then joined the Horace Silver Quintet, playing with tenor saxophonist Junior Cook, bassist Gene Taylor, and drummer Roy Brooks. Mitchell stayed with Silver's group until the band's break-up in 1964, after which Mitchell formed a group with members from the Silver quintet, substituting the young pianist Chick Corea for Silver and replacing Brooks, who had fallen ill, with drummer Al Foster. This group produced a number of records for Blue Note. It disbanded in 1969, after which Mitchell joined and toured with Ray Charles until 1971.

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