He was born in New Haven Connecticut in 1955. He began playing guitar at the age of 14 first playing rock music, progressing to blues, then to jazz, free jazz and free improvisation and released his first record Wraparound (riti) in 1983. Morris has composed over 200 original pieces of music and In 2000 he began performing and recording on double bass in addition to guitar.

Since 1993 he has recorded and/or performed with among others; Matthew Shipp, William Parker, Joe and Mat Maneri, Rob Brown, Raphe Malik, Ivo Pearlman, Borah Bergman, Andrea Parkins, Whit Dickey, Ken Vandermark, DKV Trio, Karen Borca, Eugene Chadborne, Susie Ibarra, Hession/Wilkinson/Fell, Roy Campbell Jr., John Butcher, Aaly Trio, Hamid Drake, Fully Celebrated Orchestra and others. Joe has recorded for the labels ECM, Hat Hut, Leo, Incus, Okka Disc, Homestead, About Time, Knitting Factory Works, No More Records, AUM Fidelity and OmniTone and Avant.

He has toured throughout the U.S., Canada and Europe as a solo and as a leader of a trio and a quartet. Morris has lectured and conducted workshops throughout the US and Europe. He is a former member of the faculty of Tufts University Extension College and is currently on the faculty at New England Conservatory in the jazz and improvisation department. He was nominated as Best Guitarist of the year 1998 and 2002 at the New York Jazz Awards.