Stephen Morrissey was born in Montreal, Canada. Morrissey graduated with a Bachelor of Arts degree, Honours in English with Distinction, from Sir George Williams University (now Concordia University) in 1973. In 1976 he graduated with a Master of Arts degree in English from McGill University where he studied with the eminent poet Louis Dudek. Morrissey won the Peterson Poetry Award while at McGill.
In the 1970s Morrissey was associated with the Vehicule Poets, a group of young poets who organized poetry readings at Vehicule Art Gallery in Montreal. Morrissey's first book of poems, The Trees of Unknowing was published by Vehicule Press in 1978.
The Stephen Morrissey Fonds, 1963—2014, are housed at Rare Books and Special Collections of the McLennan Library at McGill University. This extensive archival collection includes literary papers, manuscripts, correspondence, diaries, notebooks, posters, photographs of poets, tape recordings of poetry readings and other papers.
Stephen Morrissey has one son, Jake Morrissey; he married poet Carolyn Zonailo in 1995. Stephen Morrissey is a member of The Writers' Union of Canada and The League of Canadian Poets.