Quinn was born in London. He studied history and the history of art at Cambridge University, and worked as an assistant to the sculptor Barry Flanagan.
Quinn emerged in the early 1990s as one of the so-called Young British Artists (yBas). He did not show in the 1988 Damien Hirst-curated Freeze exhibition which brought the yBas together for the first time (although he did once share a flat with Hirst), but did show in the Sensation exhibition of 1997 which brought the yBas into the public eye.
Like his contemporary Antony Gormley, Quinn often uses his own body to cast his sculptures. Unlike Gormley, however, Quinn retains distinguishing features, uses unusual materials such as rubber, and presents his sculptures in unconventional ways. The No Visible Means of Escape series, for example, are rubber casts of Quinn's body, some split from the feet to the neck and hung from one half of the feet.
Quinn's best known piece is probably Self (1991, recast 1996), a sculpture of the artist's head made from nine pints of his own frozen blood which he had donated over a period of five months.
As well as modelling himself, Quinn has made a series of sculptures of people either born with limbs missing or who have had them amputated. His portrait of John Sulston, who worked on the Human Genome Project, is in the National Portrait Gallery. It consists of bacteria containing Sulston's DNA in agar jelly.
Self, like many other pieces by the yBas, was bought by Charles Saatchi. There was a rumour in 2002 that the sculpture had been destroyed by builders employed to expand the kitchen for Saatchi's partner, the celebrity chef Nigella Lawson, when they unplugged the freezer in which it was being stored. This proved to be untrue, however, as the piece was exhibited intact by Saatchi when he opened his new gallery in London in 2003.