Mazur is primarily an autodidact, but she has a degree in percussion from the Royal Danish Academy of Music.

Mazur was born in New York City in 1955, from Polish and African-American parents, who moved with her to Denmark at age 6.

She learned to play the piano, but when she was 19, she took up drumming, inspired by Al Foster, Airto Moreira, and Alex Riel.

[1] Afterward, she played with Gil Evans, Wayne Shorter, Jan Garbarek,[2] and Makiko Hirabayashi.

[1] The U.S. magazine Down Beat, in 1989, 1990, 1995, 1997, 1998 and 2002 selected Mazur as a "percussion-talent deserving wider recognition".