Clifford was born in Philadelphia in 1939, and grew up in the city, attending Temple University. His family appears to have had a musical bent (drummer J.C. Moses is a cousin) and Clifford began piano lessons at 7. After a late 50's stint in the army band, Thornton moved to New York City.
He studied with trumpeter Donald Byrd in the mid-1950s and worked with various players such as tuba player Ray Draper. He played with numerous avant-garde jazz bands, appearing as a sideman on records by notable artists Archie Shepp, Pharoah Sanders, Sun Ra, and Sam Rivers. His first album, 1967's Freedom & Unity, was recorded the day after John Coltrane's funeral. It included Coltrane associate Jimmy Garrison and also marked the first recorded appearance of Joe McPhee.
Thornton was in Algiers for the 1969 Pan-African Cultural Festival of the OAU, which had an important impact on his political thought, and integrated his musical and political aims. Most of the works recorded under his own name as leader were large-form compositions 
He taught at Wesleyan University in the early 1970s; he brought many younger jazz musicians to perform on campus, giving the academic ethnomusicology world more exposure to current American music. Thought to possess radical political leanings, Thornton was denied entry into France in the 1970's. Thornton spent the last 15 years of his life in Europe; he died in Geneva, Switzerland, in 1989.
- 1967: Freedom & Unity (Unheard Music Series) with Karl Berger, Jimmy Garrison, John McCortney, Joe McPhee, Don Moore
- 1969: Ketchaoua (BYG Actuel) with Dave Burrell, Claude Delcloo, Earl Freeman, Beb Guérin, Arthur Jones, Grachan Moncur III, Sunny Murray, Archie Shepp
- 1970: The Panther and the Lash with François Tusques, Beb Guérin, Noel McGhie
- 1972: Communications Network (Third World Records) with Jerome Cooper, Jayne Cortez, Nathan Davis, Jerry Gonzalez, Jay Hoggard, L. Shankar, Sirone
- 1974: The Gardens of Harlem (JCOA) with Roland Alexander, Carla Bley, Pat Patrick, Marvin Peterson, Dewey Redman, Wadada Leo Smith, Bob Stewart, Carlos Ward
With Dave Burrell
- Echo (1969)
With Archie Shepp
- Coral Rock
- Black Gipsy
- Attica Blues
- Archie Shepp and the Full Moon Ensemble
- Live at the Pan-African Festival
- Yasmina, a Black Woman
- Pitchin Can
Jason Guthartz's discography, compiled through 2008, is the most complete on-line listing of Clifford on record.
- Valerie Wilmer "As Serious As Your Life", 1977; LOC 99-63595
- Atavistic Worldwide: Freedom & Unity Notes
- Point of Departure