Poindexter began on clarinet and switched to playing alto and tenor sax growing up. In 1940 he studied under Sidney Desvigne, and following this attended Candell Conservatory in Oakland, where he based himself. From 1947 to 1950 he played with Billy Eckstine. In 1950 he played in a quartet with Vernon Alley, from 1951 to 1952 he was with Lionel Hampton and in 1952 he played with Stan Kenton. Neal Hefti wrote the tune "Little Pony", named after Poindexter, for the Count Basie Orchestra.
Through the end of the 1950s Poindexter played extensively both as a leader and as a sideman, recording with Charlie Parker, Nat King Cole, T-Bone Walker and Jimmy Witherspoon. From 1961 to 1964, he played backup for Lambert, Hendricks and Ross, who together also recorded a vocal version of "Little Pony". He was one of the first bebop saxophonists to begin playing soprano saxophone early in the 1960s, and recorded with Eric Dolphy and Dexter Gordon on a session for Epic Records around 1962. In 1963 he moved to Paris; while there he recorded with Ross, Phil Woods, Lee Konitz and Leo Wright. He later moved to Spain and then to Mannheim, Germany; in 1977 he returned to San Francisco and recorded again. In 1980 he took jazz singer Laurie Antonioli on his final tour. During their eight month sojourn performing in Germany, Austria, Belgium and Switzerland, Antonioli and Poindexter were a few days away from going to Paris to record with Kenny Drew (August 28, 1928 – August 4, 1993) when Poindexter suffered a stroke. Antonioli returned him to San Francisco. Having lost the ability to play saxophone, he still could sing and Antonioli performed with him in 1986, his final performance at Bajone's nightclub in San Francisco. He published an autobiography, Pony Express, in 1985, but had been largely forgotten in America by the time of his death in 1988.
- Lambert, Hendricks & Ross: The Hottest Group in Jazz (Columbia, 1959–62)
- Wes Montgomery, Buddy Montgomery, Monk Montgomery: Far Wes (Pacific Jazz, 1958–59)
- Pony's Express (Koch, 1962) with Eric Dolphy, Gene Quill, Sonny Red, Phil Woods, Jimmy Heath, Clifford Jordan, Sal Nistico, Pepper Adams, Ron Carter, Elvin Jones
- Pony Poindexter Plays the Big Ones (New Jazz, 1963)
- In Barcelona (Fresh Sound Records, 1972)