Nutter was born in Topeka, Kansas, under the given name Gilbert Warren Nutter. He is usually formally referred to as G. Warren Nutter and often casually referred to as Warren or Warren Nutter, because he preferred to be addressed by his middle name, Warren. Warren eventually settled in Chicago, Illinois where his education at the University of Chicago was interrupted by service in the U.S. Army infantry in the European Theatre in World War II. He earned the Bronze Star with oak leaf cluster (which means that he received the Bronze Star twice) and the Combat Infantryman Badge. After serving in U.S. Army Intelligence after the fall of Nazi Germany, he returned to finish his studies at the University of Chicago where he earned his B.A. (1946), M.A. (1948), and Ph.D. (1949) in economics, which he studied with Milton Friedman and Frank Knight.
While finishing his Ph.D. at the University of Chicago, he lectured in Economics and German at Lawrence College (now Lawrence University) in Appleton, Wisconsin. He later was an Associate Professor of Economics at Yale University (1950–1956), then Professor of Economics at the University of Virginia (1956–1979) until his death after a prolonged bout with colon and liver cancer in 1979.
His academic career was twice more interrupted by public service. First, in 1951 during the Korean War, Nutter was called to duty from the U.S. Army Reserves; he served in the Central Intelligence Agency. Later, from 1969–1973, he served as Assistant Secretary of Defense for International Security Affairs during the first administration of President Richard M. Nixon.