Zimunya was born in Umtali, Rhodesia (now Mutare, Zimbabwe), to Mandiera Watch and Kufera Zimunya. He graduated with honours at the University of Kent, Canterbury, UK, with a Bachelor's degree in 1978. The following year he was awarded a Master's degree, also by the University of Kent. In 1980, he returned to newly independent Zimbabwe where he settled and married Viola Catherine, and took a University of Zimbabwe position as a professor of English that he kept since.
In 1992 he received a Fulbright scholarship to the Pratt Institute in New York, USA.
Zimunya's poetry is lyrical in its love of both the natural environment and humankind, but much of his work is also highly political. He writes bitingly of the 'Benzocrats' who enriched themselves in the name of Independence, carried by the people they claimed to be liberating. Most of his published work is in English, but he also writes in Shona.