He was educated at the Shady Side Academy, After graduating from high school in 1944, he enlisted in the Air Force and spent the remainder of World War II in the aviation cadet training program. Following the war, he attended the University of Pennsylvania for an undergraduate degree and earned his law degree from the University of Pittsburgh.
Duggan was elected Allegheny County District Attorney in 1964, and re-elected in 1967 and 1971. During Duggan's 10-year tenure as DA there were few prosecutions for gambling. Duggan's predecessor in the DA's office was Democrat Edward "Easy Going Eddie" Boyle. Unlike his predecessor, Duggan was born to an affluent family, with an estate in nearby Ligonier Township, Westmoreland County.
He married his longtime partner, socialite Cordelia Scaife May, an heiress to the Mellon fortune, on August 23, 1973 in Las Vegas.
Thornburgh obtained an indictment on March 5, 1974. That same day, Duggan was found shot to death on his family estate in Ligonier Township, victim of a shotgun blast. The body was found on the grounds of the estate; the shotgun was seven to ten feet from the body. Duggan, authorities said, apparently had been hunting before accidentally or purposefully turning the shotgun on himself. The Pittsburgh Press asked, "Was the law closing in on Robert W. Duggan so inexorably that his only escape was suicide?"