Griffin began playing woodwinds at Du Sable High School in Chicago, and after graduation he toured with Lionel Hampton (Hampton, Lionel)'s big band (1945–47) and with trumpeter Joe Morris (1947–50). After two years in a U.S. Army band (1951–53), Griffin played in Chicago and then New York, where he established a national reputation playing with Art Blakey (Blakey, Art) (1957) and Thelonious Monk (Monk, Thelonious) (1958). Together with tenor saxophonist Eddie “Lockjaw” Davis, he led a quintet in 1960–62, before moving to France in 1963. He then maintained an active career touring European jazz centres, soloing with the Kenny Clarke (Clarke, Kenny)–Francy Boland big band in the 1960s and, from 1978, leading his quartet in annual American tours.

Griffin's tenor saxophone improvising was in a transitional style that fused swing and bebop elements. In earlier recordings, such as A Blowing Session (1957) and Way Out! (1958), he was noted for his creativity and technical dexterity, even while creating on complex harmonic structures (chord changes) at fast tempos. Later recordings demonstrated his sustained mastery in long solos and his instinct for building solos in classic forms while maintaining his instrumental mastery.