Locksley Wellington Hampton was born April 21, 1932 in Jeannette, Pennsylvania, the youngest of the twelve children Laura and Clarke "Deacon" Hampton raised as a working family band. The Hamptons moved to Indianapolis in 1938, and by twelve Slide was playing trombone in the family group, billed as the Duke Hampton Band, on the Indiana Avenue circuit that also produced Wes Montgomery and Freddie Hubbard. Two of his sisters, Dawn Hampton and Virtue Hampton Whitted, became working musicians in their own right, and Virtue's son, trumpeter Pharez Whitted, is his nephew. The instrument he was handed as a child had been set up backwards, so he learned to work the slide with his left hand and the bell with his right. Nobody corrected him, and he remained one of the very few left-handed trombonists in jazz for the next seven decades. In 1952, at twenty, he was on the Carnegie Hall stage with the Lionel Hampton band (no relation).

Hampton spent 1955 and 1956 in Buddy Johnson's rhythm and blues orchestra, then joined Maynard Ferguson from 1957 to 1959, where the arranging talent that would define the rest of his career first got a national hearing. He wrote "The Fugue," "Three Little Foxes," "Slide's Derangement," "Frame for the Blues" and "Newport" for the Ferguson book, charts that stayed in the band's library long after he left. In 1958 he took part in Melba Liston's trombone-choir date Melba Liston and Her 'Bones for MetroJazz. Through the same stretch he was writing and playing for bands led by Art Blakey, Tadd Dameron, Barry Harris, Thad Jones, Mel Lewis and Max Roach.

He left Ferguson in the autumn of 1959 and put together his own octet, a two-trumpet, tuba-bottomed group pitched somewhere between a small band and a miniature orchestra. Its first date, Slide Hampton and His Horn of Plenty, was cut in New York in 1959 with Booker Little and Freddie Hubbard on trumpets and George Coleman on tenor, though Strand did not issue it until 1961. Atlantic then recorded the group four times in three years: Sister Salvation (recorded February 11 and 15, 1960 at Bell Sound Studios with Artie Shaw producing), Somethin' Sanctified (recorded October 17, 1960, with Larry Ridley on bass), Jazz with a Twist and Explosion! The Sound of Slide Hampton, both 1962. That same year Epic released Drum Suite, a five-part large-ensemble piece built around percussion. The octet toured the United States and Europe and functioned as a finishing school: Hubbard, Coleman and Little all passed through it on the way to careers of their own.

A 1968 tour with Woody Herman's orchestra took Hampton to Europe, and he stayed nine years. He based himself largely in Germany and worked constantly as soloist, writer and guest director: A Day in Copenhagen with Dexter Gordon for MPS in 1969, the four-trombone Trombone Workshop with Albert Mangelsdorff, Ake Persson and Jiggs Whigham, big-band dates with Sweden's Umea Big Band at Montreux, with Vaclav Zahradnik's orchestra in Prague and with Joe Haider in Munich, plus recordings alongside Art Farmer, Dusko Gojkovic, Oliver Nelson's Berlin Dreamband, and the French singers Sacha Distel and Claude Nougaro. He also turned up on Charles Mingus sessions on either side of the European years, starting with the 1960 dates issued as Pre-Bird / Mingus Revisited.

Hampton came home in 1977 and immediately delivered one of his best-known pieces of writing: the arrangements for Dexter Gordon's Sophisticated Giant on Columbia, an eleven-piece setting built around Gordon's return to American recording. He took up teaching, serving as artist-in-residence at Harvard in 1981 and holding posts at the University of Massachusetts Amherst, DePaul University and in Indiana. In 1979 he launched World of Trombones, a standing band of nine trombones and rhythm section that became his signature vehicle, and he co-led Continuum, a quintet with Jimmy Heath devoted to the compositions of Tadd Dameron, documented on 1983's Mad About Tadd. Leader dates continued through the 1980s, among them Roots for Criss Cross in 1985 with Clifford Jordan, alongside sideman and arranging work for McCoy Tyner's big band, Sam Jones, Louis Hayes, Philly Joe Jones and Woody Shaw.

The last three decades of his working life were bound up with Dizzy Gillespie and Gillespie's legacy. Hampton played in the United Nation Orchestra, shared musical direction of the year-long Diamond Jubilee celebration of Gillespie's seventy-fifth birthday with Paquito D'Rivera, and in February 1993, weeks after Gillespie's death, recorded Dedicated to Diz live at the Village Vanguard with a band billed as the Jazz Masters, featuring Jimmy Heath, Jon Faddis, Steve Turre, Danilo Perez, George Mraz and Lewis Nash. He kept writing for the Dizzy Gillespie All-Star Big Band into the 2000s and served as musical advisor to the Carnegie Hall Jazz Band. His arranging finally brought him a Grammy in 1998, for "Cotton Tail" on Dee Dee Bridgewater's Dear Ella, in the Best Jazz Arrangement Accompanying Vocalist(s) category. A second followed in 2005, when the Vanguard Jazz Orchestra's The Way: Music of Slide Hampton took Best Large Jazz Ensemble Album, and his "Stardust" chart for the Dizzy Gillespie All-Star Big Band drew a further nomination in 2006. The National Endowment for the Arts named him an NEA Jazz Master in 2005, the same year the Indianapolis Jazz Foundation put him in its Hall of Fame.

Hampton kept working into his eighties. He recorded Spirit of the Horn with World of Trombones and guest Bill Watrous for MCG Jazz in 2002, debuted a self-funded Slide Hampton Ultra-Big Band at the Tribeca Performing Arts Center on June 4, 2006, and in 2009 completed a four-part suite titled "A Tribute to African-American Greatness." He also stayed available for younger players' first records: in 2008 he shared the trombone chair on Israeli trombonist Jonathan Voltzok's debut More to Come for Kol Yo Records, with Antonio Hart, Aaron Goldberg, Barak Mori and Ali Jackson. The Jazz Foundation of America gave him its Lifetime Achievement Award in June 2021. He passed away at his home in Orange, New Jersey on November 18, 2021, at 89.

Hampton played bebop trombone at a level almost nobody matched: fast, articulate, harmonically exact, delivered on an instrument whose slide makes bebop tempos physically punishing, and with the added handicap of a backwards, left-handed setup nobody ever bothered to correct. Gary Giddins called him "perhaps the most underrated bebop virtuoso soloist alive." His writing is what spread his name furthest. Hampton's ear was for weight and color in the low and middle register: the tuba-anchored octet, the nine-trombone World of Trombones, the Maynard Ferguson charts, the eleven-piece Dexter Gordon settings on Sophisticated Giant, all take a small number of horns and make them sound like a full orchestra without thinning the swing. He was a direct link between Tadd Dameron's compositional bebop and the arrangers who came after, and his charts remain standing repertoire for the Vanguard Jazz Orchestra and for college big bands across the United States.