Pizzi's first instrument was clarinet. He attended the Boston Conservatory and Berklee College of Music in the 1960s, and taught in Randolph, Massachusetts public schools from 1964 to 1969. He relocated to California in 1969, and in the 1970s worked with Thad Jones and Mel Lewis, Frank Zappa, Shelly Manne, Willie Bobo, Moacir Santos, Mark Levine, and Dizzy Gillespie. In the 1980s he accompanied Nancy Wilson and was a sideman for Milcho Leviev and Bob Florence, and worked with the American Jazz Orchestra into the early 1990s. He has recorded as a leader, including in a quartet setting under the ensemble name Windrider. He joined the faculty at the Mancini Institute in 1997.