Born in Franklin, Indiana on December 28, 1923, he was raised in Texas and went to college at Indiana University. There, on a speech and drama scholarship, he began to act and perform however this was interrupted by being called into the service. In World War II where he saw action overseas, he was befriended by actor Melvyn Douglas, who led his division. With such encouragement, as well as meeting and becoming familiar with some Broadway folks, Duggan went into acting. From 1953 onward, he was a fixture in both movies and television.

Most notably, he played General Ed Britt on 12 O'Clock High (1964), he was Cal Calhoun in Bourbon Street Beat (1959) and his most famous role as "Murdoch Lancer" in Lancer (1968) and the original John Walton opposite Patricia Neal in The Homecoming: A Christmas Story (1971). He was "Howitzer Al Houlihan", the father of "Hotlips Houlihan" (Loretta Swit) in M*A*S*H (1972). In 1954, he wed Broadway actress Elizabeth "Betty" Logue. After their deaths, they were cremated and their ashes scattered at Lake Arrowhead, California.