Plimpton was educated at Phillips Exeter Academy, Amherst College, and Harvard Law School, where he was a roommate of Adlai Stevenson.
On a recommendation from Felix Frankfurter, Plimpton began writing editorials on legal issues for the New York World for Walter Lippmann while still at Harvard.
In 1926, he married Pauline, the daughter of the botanist Oakes Ames; they had four children, one of whom was George Plimpton, a writer and founder of the Paris Review.
From 1968 to 1970, Plimpton also served as president of the New York City Bar Association, where he became involved in the political debates of the late 1960s, particularly over the Vietnam War.
He was a member of the board of the New York Philharmonic, the Foreign Policy Association, the American-Italy Society, Roosevelt Hospital and the Metropolitan Museum of Art, where he was instrumental in securing the acquisition of the Temple of Dendur.