Purdy, who grew up in small Ohio towns, was educated at the Universities of Chicago and Puebla (Mexico). He served as an interpreter and taught for a few years before turning to writing full-time. His first two works—Don't Call Me by My Right Name and Other Stories and 63: Dream Palace, a novella (both 1956)—were rejected by a number of American publishing houses and were first published by Purdy through a subsidy publisher. These books won the support of Dame Edith Sitwell and, following their publication in England, met with critical acclaim in America as well.

Purdy's fiction examines the relationships between individuals and the effects of family life. Malcolm (1959) tells the story of the experiences of a 15-year-old boy in a fruitless search for his identity. In Purdy's later works, such as The Nephew (1960) and Cabot Wright Begins (1964), he further develops the bleak worldview that he first propounded in Malcolm. In his trilogy, Sleepers in Moon-Crowned Valleys—consisting of Jeremy's Vision (1970), The House of the Solitary Maggot (1974), and Mourners Below (1981)—Purdy explores small-town American life and destructive family relationships.

Although critical response to Purdy's work was mixed, he was generally considered a powerful writer and an original, skillful black humorist. His novels include I Am Elijah Thrush (1972) and In a Shallow Grave (1975). Purdy also published story collections, plays, and poems. His novel Gertrude of Stony Island Avenue (1998), about a woman's reaction to her artist-daughter's death, received considerable critical acclaim.