David Keith Murray was born February 19, 1955, in Oakland, California, and grew up in Berkeley. His father, Walter Pendleton Murray, was a guitarist, sanitation worker, and a founding deacon of the Missionary Church of God in Christ on Allston Way in Berkeley, where his mother played organ. Murray was handed an alto saxophone at around age nine by his teacher, Phil Hardymon, at Longfellow Elementary School, and played his first notes on it at that same church around 1965. Hearing Sonny Rollins on record pulled him toward the tenor, the horn on which he built his career, though he never gave up the bass clarinet, an instrument he did as much as anyone of his generation to establish as a serious solo voice in jazz.

He enrolled at Pomona College in Claremont, California, in 1973, where he studied with the critic Stanley Crouch and trumpeter Bobby Bradford and began an independent-study project interviewing avant-garde figures including Ornette Coleman, Cecil Taylor, John Cage, and McCoy Tyner. It was saxophonist Dewey Redman who reportedly told him to put down the pencil and pick up the horn. In September 1975, midway through college, Murray moved to New York with Crouch, taking a loft above the Tin Palace at Second Street and the Bowery that the two men called Studio Infinity, and plugged directly into the loft-jazz scene then centered on that stretch of the Lower East Side. His first recording as a leader, Flowers for Albert (India Navigation, recorded June 26, 1976, at the Ladies' Fort in lower Manhattan), was a tribute to Albert Ayler, cut with trumpeter Olu Dara, bassist Fred Hopkins, and drummer Phillip Wilson when Murray was 21.

Later that year he traveled to New Orleans for a series of clinics organized by Ed Jordan at Southern University, where the enthusiastic response to an unaccompanied-saxophone format convinced Murray, Julius Hemphill, Oliver Lake, and Hamiet Bluiett to formalize it as the World Saxophone Quartet; the group's debut, Point of No Return (Moers Music, 1977), launched a cooperative that would record and tour for decades, threading free jazz together with R&B, funk, and South African township influences. Through the 1980s Murray built out a parallel body of work as a composer and bandleader on the Italian Black Saint and Soul Note labels: the octet records Ming (1980, with Henry Threadgill, Olu Dara, Lawrence "Butch" Morris, George Lewis, Anthony Davis, Wilber Morris, and Steve McCall), Home (1982), and Murray's Steps (1983), followed by his first big-band record, Live at Sweet Basil, Volume 1 (1984). In the same period he co-founded the Music Revelation Ensemble with guitarist James Blood Ulmer, bassist Amin Ali, and drummer Ronald Shannon Jackson, a free-funk unit whose 1980 Moers Music debut, No Wave, grew out of Ulmer's standing in New York's punk and no-wave scene (the band played CBGB and opened for Public Image Ltd.), and he joined clarinetist John Carter's Clarinet Summit alongside Alvin Batiste and Jimmy Hamilton, documented on In Concert at the Public Theater (1981) and Southern Bells (recorded 1987).

Murray's discography crosses into the mainstream jazz establishment as well: he was one of two tenors, alongside Pharoah Sanders, on pianist McCoy Tyner's all-star Blues for Coltrane: A Tribute to John Coltrane (Impulse!, recorded July 9, 1987), which won the Grammy Award for Best Jazz Instrumental Performance. In September 1993 he sat in with the Grateful Dead at Madison Square Garden, communicating with Jerry Garcia, Bob Weir, and Phil Lesh through the band's in-ear monitor system, and returned for a Jerry Garcia Band date at the Garden that November and a Grateful Dead show at the Oakland Coliseum in February 1995; after Garcia's death he recorded the tribute album Dark Star: The Music of the Grateful Dead (1996). Drummer Rashied Ali appears on Murray's Body and Soul (Black Saint, recorded February 11-12, 1993, at Sear Sound in New York, with pianist Sonelius Smith, bassist Wilber Morris, and vocalist Taana Running); the album's closing duo between Murray and Ali, "Cuttin' Corners," was deliberately built to recall Ali's earlier duo with John Coltrane, Interstellar Space.

Murray signed with the Canadian label Justin Time in 1995 and made his debut for it with Fo Deuk Revue (recorded in Dakar, Senegal, June 1996; released 1997), an ambitious fusion of jazz, funk, Afro-pop, and rap featuring Senegalese percussionist Doudou N'Diaye Rose, the rap duo Positive Black Soul, and spoken-word passages by poet Amiri Baraka. Around the same time he fell in love with Valerie Malot, a French booking agent and music-industry organizer, and by the late 1990s had relocated to Paris, where he spent roughly two decades based, working extensively with musicians from Guadeloupe, Martinique, and Francophone West Africa; Creole (1998) was recorded in Guadeloupe in October 1997, and Murray and Malot went on to co-found the booking agency 3D Family. Honors accumulated across the decades: the Village Voice named him Musician of the Decade for the 1980s, he won the Down Beat-affiliated Bird Award in 1986, received a Guggenheim Fellowship in 1989 and the Danish Jazzpar Prize in 1991, was Newsday's Musician of the Year in 1993, received an honorary doctorate from Pomona College in 2012, and won a legacy grant from the California Arts Council in 2021. He remains active into his seventies: Francesca (2024), a quartet date with pianist Marta Sanchez, bassist Luke Stewart, and drummer Russell Carter, was named the second-best jazz album of the year by the New York Times, and Birdly Serenade, a new quartet recording, followed on Impulse! in 2025.

Murray came up in the wake of the Coltrane-influenced generation but deliberately built a different tenor sound, citing not just Albert Ayler, Ornette Coleman, and Archie Shepp as formative influences but also older mainstream stylists, Coleman Hawkins, Ben Webster, and Paul Gonsalves, whose vibrato-heavy, big-toned "tough tenor" vocabulary he folded into an otherwise avant-garde attack. That hybrid, capable of swinging hard, honking and screaming, and playing tender ballads within the same solo, plus a command of circular breathing that let him sustain enormous unbroken phrases, made him one of the most versatile and prolific saxophonists to emerge from the loft-jazz generation. He was equally influential as a bass clarinetist, doing more than any player since Eric Dolphy to make the instrument a viable solo voice in jazz, and as an organizer: cooperative or co-led units he helped found, the World Saxophone Quartet, the Music Revelation Ensemble, Clarinet Summit, gave him a foothold across free jazz, funk-inflected fusion, and chamber-style reed ensembles simultaneously, while his octet and big-band writing carried forward the large-ensemble compositional tradition of Charles Mingus and Duke Ellington into an avant-garde idiom.