Mohorcic was a 30-year-old rookie when he reached the Rangers in 1986 and tied a major-league record for relief pitchers by appearing in 13 consecutive games that August. Manager Bobby Valentine let him pitch to one batter with a six-run lead in the 13th game.
Mohorcic led the Rangers with 16 saves and a 2.99 ERA in 1987 while appearing in 74 games. He underwent elbow surgery in March 1988, and was 0-6 (7.67) in his last 30 appearances when he was traded to the Yankees for Cecilio Guante that August 30. The 1990 season, spent with the Montreal Expos, was his last in the majors.
In 1988, Mohorcic was accused of doctoring the ball during a game in Milwaukee. The umpire found no evidence of wrongdoing, but Mohorcic later complained of a sore throat and was admitted to a hospital with internal bleeding, where it was discovered that he had swallowed a piece of sandpaper.
The Cleveland native was named after Indians outfielder Dale Mitchell.