Assenmacher was signed by the Braves out of a 1983 tryout camp. As a rookie in 1986, he went 7-3 (2.50) with seven saves in 61 appearances, mostly as a lefthanded setup man for Gene Garber. He went 8-7 with five saves in 1988, posting a 1.16 ERA away from Atlanta-Fulton County Stadium but a 4.87 ERA at home. In mid-1989 Assenmacher was acquired by the Cubs for their successful stretch drive and spent the next four years in Chicago.
Filling in for an injured Mitch Williams, Assenmacher saved ten games in 1990. When Dave Smith went down in 1991, he racked up another fifteen. But Assenmacher never again managed more than eight in a season. Firmly typecast as a situational lefty, he moved on to the Yankees in 1993 and White Sox in 1994 before settling down with Cleveland in 1995. The wily veteran provided steady relief for the Indians until bone spurs in his feet began to limit his effectiveness in 1997.