Margitza's paternal grandfather, a Hungarian Gypsy violinist, taught him to play the violin at the age of four. His father also played violin with the Detroit Symphony Orchestra. Following this he played piano and oboe, and settled on tenor sax while in Fordson high school. He attended several colleges: Wayne State University, Berklee College of Music, University of Miami and Loyola University New Orleans. He toured with Maynard Ferguson and Flora Purim in the 1980s, and moved to New York City in 1988, where he played with Miles Davis.
Between 1989 and 1991, Margitza released three sessions for Blue Note Records, and has recorded copiously thereafter, including with Eddie Gomez, Tony Williams, Bobby Hutcherson, Maria Schneider, McCoy Tyner and Chick Corea. He has also composed a saxophone concerto and two symphonies for orchestra.
- Color (Blue Note Records, 1989) U.S. Jazz #9
- Hope (Blue Note, 1990) U.S. Jazz #11
- This is New (Blue Note, 1991) U.S. Jazz #19
- Standard New (EMI, 1991)
- Hands of Time (Challenge Records, 1994)
- Work It (SteepleChase Records, 1995)
- Game of Chance (Challenge, 1997)
- Heart of Hearts (Palmetto Records, 2000)
- Memento (Palmetto, 2001)
- Bohemia (Nocturne Jazz, 2005)
- Second Home (2006)