James Minter Knepper was born in Los Angeles on November 22, 1927. His parents separated soon after his birth and he spent much of his childhood at boarding and military schools, including Page Military Academy and St. John's Military Academy, while his mother worked. He started on alto horn at six and moved to trombone at nine, and he was taking professional gigs around Los Angeles by fifteen. He later spent time at Los Angeles Community College. His first steady big-band work came with Freddie Slack in 1947, followed by the Roy Porter big band in 1948 and 1949, a young Los Angeles orchestra whose ranks also included Eric Dolphy and Art Farmer; the band's January and February 1949 Savoy sessions are Knepper's earliest issued recordings. Around the same period he was playing in a bebop group organized by Dean Benedetti, and it was there that he first met the bassist Charles Mingus.

The first half of the 1950s was journeyman big-band work: Charlie Spivak in 1950 and 1951, Charlie Barnet in 1951, then stints with Woody Herman and Claude Thornhill. He married trumpeter Maxine Helen Fields, formerly of the International Sweethearts of Rhythm, on May 8, 1954, in Tucson, Arizona, while he was on the road with Maynard Ferguson's band. He settled in New York in 1956. Mingus hired him out of the Claude Thornhill Orchestra in 1957, and that single recruitment defined the rest of his career.

The Mingus Jazz Workshop years from 1957 to 1961 produced the body of work Knepper is still best known for. In 1957 alone he recorded The Clown for Atlantic, East Coasting and A Modern Jazz Symposium of Music and Poetry for Bethlehem, and the July 18 and August 6 sessions that became Tijuana Moods, an album RCA held back until June 1962 because of a legal dispute with Mingus. He is on Blues & Roots (recorded February 4, 1959), Mingus Ah Um (May 1959), Mingus Dynasty (November 1959), Pre-Bird, also issued as Mingus Revisited (1960), the Jazz Artists Guild session Newport Rebels with Max Roach, Eric Dolphy and Roy Eldridge (November 1960), and Oh Yeah (November 1961). He was working steadily outside the Workshop at the same time. He made his own first leader dates in this stretch, spent 1959 in Stan Kenton's orchestra after Gene Roland brought him in, replaced Willie Dennis in Herbie Mann's group for a fourteen-week State Department tour of Africa that ran from December 31, 1959 to April 5, 1960, and took a trombone chair on Gil Evans's Out of the Cool, cut at Van Gelder Studio across four dates in November and December 1960.

In October 1962 the association broke down violently. Knepper was at Mingus's apartment helping prepare music for a Town Hall concert booked for October 12, and an argument over how much copying and arranging Knepper was willing to take on ended with Mingus striking him in the mouth. The blow broke off a crowned tooth and the stub beneath it, damaging his embouchure. He did not play the concert, which was a shambles for unrelated reasons as well. Mingus was charged, appeared in court in January 1963, was convicted of third-degree assault and received a suspended sentence. Knepper's own account of the blow was undramatic: he described it as a slap that happened to catch the tooth. What it cost him is the detail sources still disagree on. He lost the top octave of his range, and accounts divide between a permanent loss and a gap of roughly two years before it returned. The two men did not work together again for well over a decade.

The years that followed were the most varied of his working life. He toured the Soviet Union with Benny Goodman's big band in 1962, a trip issued as Benny Goodman in Moscow, and took long Broadway pit runs, including the full run of Funny Girl from its March 26, 1964 opening and An Evening with Marlene Dietrich in 1967 and 1968. He joined the Thad Jones / Mel Lewis Orchestra in its early years and stayed into the mid-1970s, recording Monday Night (1968), Central Park North (1969), Consummation (1970), Suite for Pops (1972) and Potpourri (1974) with the band and touring Japan, Europe and the Soviet Union. He kept working for Gil Evans through The Individualism of Gil Evans, and turned up in the era's more experimental large ensembles: Gary Burton's A Genuine Tong Funeral (1967), The Jazz Composer's Orchestra (1968) and Carla Bley's Escalator Over the Hill (1971). Chuck Israels's National Jazz Ensemble used him as a featured soloist in 1975 and 1976, the setting in which the photograph on this page was taken.

He and Mingus reconciled in the second half of the 1970s. Knepper is on Cumbia & Jazz Fusion, recorded in 1977, and on the January 1978 orchestral sessions Mingus supervised but could no longer play, issued as Me, Myself an Eye (1979) and Something Like a Bird (1980). After Mingus's death in January 1979 he became a mainstay of Mingus Dynasty, the repertory band drawn from Mingus alumni, recording Chair in the Sky with Charlie Haden, Don Pullen and Dannie Richmond, then Live at Montreux (1981), Reincarnation (1982) and the Paris concerts issued in 1988 and 1993, and taking a leading role in the group after Richmond's death in 1988. His own leader catalogue finally thickened in the same period, mostly for European independents: Cunningbird for SteepleChase in 1976, Jimmy Knepper in L.A. with Lew Tabackin and Shelly Manne in 1977, Tell Me... in the Netherlands in 1979, Primrose Path in London in 1980, 1st Place at Van Gelder in 1982, I Dream Too Much for Soul Note in 1984 and Dream Dancing for Criss Cross in 1986. He also spent 1977 to 1979 in the Lee Konitz Nonet and recorded Road Time with the Toshiko Akiyoshi / Lew Tabackin Big Band in 1976.

DownBeat's readers voted him the year's best trombonist four years running from 1981 to 1984, and its critics gave him first place repeatedly across the 1980s; 1st Place takes its title from exactly that, and early pressings carried a sticker advertising the 1986 critics' poll win. Cunningbird brought a Grammy nomination for Best Jazz Instrumental Performance, Soloist at the 23rd Annual Grammy Awards. Knepper developed Parkinson's disease in his last years and stopped performing. He passed away on June 14, 2003, in Triadelphia, West Virginia, at 75, from complications of the disease. A memorial was held at Saint Peter's Church in Manhattan on November 9, 2003.

Knepper built a bebop vocabulary on a pre-bebop foundation, taking the warm, vocalized phrasing of swing trombonists Dickie Wells and Lawrence Brown and running Charlie Parker's line construction through it, which is why he never sounded like a J.J. Johnson descendant even at comparable speed. The mechanism was technical as much as conceptual: he used altered slide positions to get legato at tempos where most trombonists have to tongue, so his fast passages phrase more like a saxophone than a brass instrument, with the slurs and small pitch inflections left in rather than cleaned up. That combination of agility and unpredictability is what Charles Mingus was buying when he hired him, and Mingus called him "probably the greatest trombone player who ever lived." He was also a composer with a real book of his own, including "Cunningbird," "Primrose Path," "Languid" and "Figment Fragment," enough of it that the Mark Masters Jazz Orchestra devoted a full album, Jimmy Knepper Songbook, to arrangements of his tunes in 1993, with Knepper himself in the trombone section.