Born in Boston, Massachusetts, Raup was educated at the University of Chicago and at Harvard, where he obtained his PhD in 1957. After a brief spell at the California Institute of Technology, Raup spent the period from 1957 to 1965 at Johns Hopkins, Baltimore, and from 1966 to 1978 as professor of geology at the University of Rochester, New York. In 1980 Raup returned to the University of Chicago as professor of geophysics.

Much of Raup's work was devoted to the problem of extinction. In 1983, in collaboration with John Sepkoski, Raup proposed the controversial thesis that extinction rates were cyclical, peaking periodically every 26 million years. The evidence for the hypothesis was derived from a large body of data collected by Sepkoski.

Initially Raup offered no explanation for such periodicity, other than to suggest that an extraterrestrial cause was more likely than a terrestrial one. Physicists were quick to take up the challenge with Richard Muller proposing the existence of a companion star of the sun, later named Nemesis, with a 26-million-year orbit, bringing with it periodic asteroid showers. Raup described the controversy which developed in his The Nemesis Affair (New York, 1986).

But, writing later in his Extinction (Oxford, 1993), he has noted that most astronomers have rejected the Nemesis and similar hypotheses. As to the 26-million-year periodicity, expert opinion is apparently evenly divided.

Raup also published, with S. M. Stanley, a widely used textbook, Principles of Paleontology (San Francisco, 1978).