Harris was born in Pittsburgh, Pennsylvania. Coming from an athletic family, he played baseball as a teenager for the Kansas City Monarchs (then part of the Negro American League) and was scouted by major league teams Brooklyn Dodgers and New York Giants.
It was only after he was in the army that he began playing drums. After his national service ended in 1963 he moved to New York City and was encouraged to pursue a musical career by Max Roach. While in New York he worked and/or toured with Marion Brown, Dexter Gordon, Albert Ayler, Joe Henderson, Freddie Hubbard, Clifford Jordan, Howard Johnson, Sheila Jordan, Lee Konitz, Thelonious Monk, Roswell Rudd, Sonny Rollins, McCoy Tyner, Sonny Stitt, Clark Terry, Chet Baker, Doc Cheatham and Larry Coryell among other musicians.
In addition, Harris founded a "world music" band and called it "The 360 Degree Music Experience". The band included some of the most significant artists of the time, including Buster Williams, Hamiet Bluiett, Don Pullen, Jimmy Garrison, Ron Carter, Ricky Ford, Titos Sompa and many others.
Harris died of prostate cancer in New York at the age of 55. His children, William Godvin Harris III, Verna Harris Vaughn, and Portia Harris.
- 1975: From Ragtime to No Time
- 1976: In: Sanity (Black Saint, 1976)
- 1978: African Drums (Owl)
- 1979: Beautiful Africa (Soul Note)
- 1979: Negcaumongus - with Don Pullen, Hamiet Bluiett, Ricky Ford, Francis Haynes, Ken McIntyre, Cameron Brown
- 1979: Live at Nyon (Cadence Jazz Records)
- 1980: 360° Experience - A Well-Kept Secret - with Don Pullen, Bill Warnick, Greg Williams, Willie Ruff, Candido Camero, Sharon Freeman, Hamiet Bluiett, Ricky Ford, Buster Williams, Francis Haynes
- 1983: Beaver Is My Name (Timeless Records)
With Albert Ayler
- Lörrach, Paris 1966
- Stockholm, Berlin 1966'
With Marion Brown
- Three for Shepp (Impulse!, 1966)
With Ken McIntyre
- Chasing the Sun (SteepleChase, 1979)
With Roswell Rudd
With Archie Shepp
- Archie Shepp Live in San Francisco (Impulse!, 1966)
- Mama Too Tight (Impulse!, 1966)
- The Magic of Ju-Ju (Impulse!, 1967)
- The Way Ahead (Impulse!, 1968)
- For Losers (Impulse!, 1971)
- The Cry of My People (1972)
- Body and Soul (1975)
- Steam (1976)
- A Sea of Faces (1975)
- Montreux Two (1975)
- Montreux One (1975)
- Jazz a Confronto 27 (1975)
- Allmusic biography
- Pareles, Jon. "Beaver Harris, 55, A Leading Drummer in Jazz Ensembles". The New York Times, January 7, 1992.