Vázquez was born in 1958 in Philadelphia, Pennsylvania. After spending his early years in Puerto Rico, he grew up in the heart of North Philadelphia's Puerto Rican community. He bought his first trombone from a friend for $5 and joined the elementary school band.
Vázquez has always been deeply moved by jazz, and specifically cites the music of John Coltrane and J.J. Johnson as having most influenced him. In addition, his appreciation for and knowledge of the indigenous music of the Caribbean peoples provides him with a unique ability to fuse Afro-Caribbean rhythms, specifically those from Puerto Rico, with freer melodic and harmonic elements of progressive jazz.