Richard Allen Mitchell was born on March 13, 1930, in Miami, Florida, and grew up there. He picked up the trumpet at 17 to join his high school band, and the nickname "Blue" came with it. His early heroes were Dizzy Gillespie, Fats Navarro, Miles Davis, Kenny Dorham, and Clifford Brown, and he later credited a Miami trumpeter and bandleader, Dick Smothers, with the lyrical streak that became his signature. As a teenager he played bebop repertoire at a Miami Beach club with the bassist Sam Jones, a friendship that lasted: the two recorded together on and off until Mitchell's last years.

After high school he worked with local players in Miami, and at Jones's urging he joined the touring orchestra of the saxophonist Paul Williams in Detroit, which he later described as his first tour with a professional band. While that tour passed through New York in 1952 he made his first recordings, sides that came out years later on Lou Donaldson's Blue Note compilation Quartet/Quintet/Sextet. He stayed in New York and spent 1952 to 1955 in saxophonist Earl Bostic's touring rhythm-and-blues band, where he met Benny Golson; AllMusic and the Blue Note label's biography also name Chuck Willis among the R&B leaders he played for in these years. In 1955 he returned to Miami, where his fellow Floridian Cannonball Adderley heard him and recommended him to Orrin Keepnews, the producer of Riverside Records. Keepnews flew to Miami to hear him and signed him to record a series of his own albums.

Mitchell recorded with Adderley on Portrait of Cannonball in July 1958 and cut his own debut, Big 6, on July 2 and 3, 1958, at Plaza Sound Studios in New York, with trombonist Curtis Fuller, tenor saxophonist Johnny Griffin, pianist Wynton Kelly, bassist Wilbur Ware, and drummer Philly Joe Jones. Six more Riverside leader albums followed through 1962, most of them built around Kelly's piano: Out of the Blue (January 5, 1959, with Benny Golson, Art Blakey, and Paul Chambers or Sam Jones), Blue Soul (September 1959, with Curtis Fuller and Jimmy Heath), the quartet set Blue's Moods (August 24 and 25, 1960), the strings-and-brass session Smooth as the Wind (December 1960 and March 1961, with arrangements by Tadd Dameron and Benny Golson), and A Sure Thing (March 1962, with Heath's charts and Clark Terry as a second trumpet). In August 1962 he recorded The Cup Bearers with Junior Cook, Gene Taylor, and Roy Brooks, his colleagues from the Horace Silver Quintet, plus pianist Cedar Walton.

In 1958 Mitchell had joined the Horace Silver Quintet, alongside tenor saxophonist Junior Cook and bassist Gene Taylor, with drummer Louis Hayes and later Roy Brooks, and he stayed until the group broke up in March 1964. The quintet's records from these years include Finger Poppin' (1959), Blowin' the Blues Away (1959), Horace-Scope (1960), Doin' the Thing (1961, a live set), The Tokyo Blues (1962), Silver's Serenade (1963), and Song for My Father (1963 and 1964). When Silver dissolved the band, Mitchell kept most of it together under his own name, with Cook and Taylor, the young pianist Chick Corea in Silver's chair, and drummer Al Foster replacing Brooks. The new group's first Blue Note album was The Thing to Do (July 30, 1964), followed by Down with It! (July 14, 1965), Bring It Home to Me (January 6, 1966, with pianist Harold Mabern and drummer Billy Higgins), Boss Horn (November 17, 1966, an octet date with Duke Pearson's arrangements), and Heads Up! (November 17, 1967, with McCoy Tyner on piano). The group, with changing personnel, lasted until 1969; a separate August 13, 1963 session with Leo Wright, Joe Henderson, Herbie Hancock, Gene Taylor, and Brooks, Step Lightly, stayed in the Blue Note vault until 1980. In these same years Mitchell was a regular horn in Blue Note and Prestige sessions led by others, among them dates by Lou Donaldson, Stanley Turrentine, Jackie McLean, Jimmy Smith, and Hank Mobley.

His Blue Note leader albums turned toward soul and funk at the end of the decade. Collision in Black (September 1968) and Bantu Village (May 1969) were recorded in Los Angeles with the saxophonist, pianist and arranger Monk Higgins and a studio band. From 1969 to 1971 Mitchell toured with Ray Charles, and he is on the Ray Charles album My Kind of Jazz (January 1970). From 1971 to 1973 he played with the English blues bandleader John Mayall, appearing on Jazz Blues Fusion and the albums after it. During those years he also recorded for Bob Shad's Mainstream label, starting with Blue Mitchell (March 1971) and continuing through Vital Blue, Blues' Blues, The Last Tango = Blues, Graffiti Blues (March 1, 1973), and Many Shades of Blue (1974).

Mitchell moved to Los Angeles in 1974 and worked there as a studio musician in jazz, R&B, soul, rock, and funk. He played big-band dates under Louie Bellson, Bill Holman, and Bill Berry, and was principal soloist for Tony Bennett and Lena Horne. His own records in these years were the RCA albums Stratosonic Nuances (1975) and Funktion Junction (1976), and he took part in the Xanadu sessions that produced True Blue and Silver Blue (October 1976) with Al Cohn, Dexter Gordon, and Sam Noto. From 1975 to 1978 he co-led a quintet with the tenor saxophonist Harold Land, which recorded Mapenzi for Concord on April 14, 1977. Two weeks later he cut the quintet date Stablemates (April 28 and 29, 1977), and the Impulse! albums African Violet and Summer Soft, recorded in 1977, came out in late 1977 and early 1978. Cancer forced him to stop playing in October 1978, and he passed away in Los Angeles on May 21, 1979, at 49.

Mitchell was a lyrical, even-tempered trumpeter with a clear, lightly swinging tone, and he was happiest on ballads and in relaxed tempos. AllMusic called his sound direct and lightly swinging, a natural fit for the hard bop of Blue Note in the 1960s, and observed that he is often overlooked because he never stood out vividly from the crowd; the jazz.com encyclopedia calls him one of the most underappreciated contributors to hard bop and notes that his lines were rounder and more restrained than those of Clifford Brown, the model for most trumpeters of his generation. His years with Horace Silver taught him to work a tune until it was ready: the pieces on The Thing to Do were reportedly tightened over eight separate performances before the recording session, a practice he said he got from Horace. He is credited as the most recorded trumpeter in jazz-organ settings, with 27 sideman recordings, and his late-1960s and 1970s albums moved into soul jazz and jazz-funk, output that the jazz.com encyclopedia calls uneven. Jimmy Heath called him one of the most melodic players of his generation. His Los Angeles years combined funk and pop-jazz studio albums with straight-ahead quintet work alongside Harold Land.