Deegan was born in Camden, New Jersey. His umpiring career began in the Midwest League in . He also worked in the Carolina and Southern Leagues prior to becoming a major league umpire in . In the majors, he officiated in four American League Championship Series: 1970 (Game One only), 1974, 1977 and 1984. He also umpired in the 1978 All Star Game and the 1976 World Series; he was the home plate umpire for Game Four of the Series, which the defending champion Cincinnati Reds won on the strength of Johnny Bench's two-home run, five-RBI performance to complete a sweep of the New York Yankees. In that game, first base umpire Bruce Froemming ejected Yankees' manager Billy Martin after Martin threw a baseball at Deegan.