Crump worked for many years as a government deer-culler in areas of New Zealand native forest. He collected his experiences in his first novel A Good Keen Man in 1960. This novel became one of the most popular in New Zealand history, and Crump’s success continued with the more fictional Hang on a Minute Mate (1961), One of Us (1962), There and Back (1963), Gulf (1964), A Good Keen Girl (1970), Bastards I Have Met (1971), and others. Crump was also well known for appearing in a series of acclaimed New Zealand television advertisements for Toyota’s four-wheel drive cars, which relied on his image as a stalwart "bushman". He played an archetypal Kiwi bloke in the 1964 New Zealand film Runaway. Crump's song, "Side By Side", featuring his "sidekick" Scotty (broadcaster Lloyd Scott), was used as the theme song for Team New Zealand in the America's Cup.
He married five times, including a one-year marriage to the poet Fleur Adcock and a twelve year marriage to Robin Lee-Robinson, and had six sons.