Assenmacher attended Aquinas High School where he was teammates with Jeff Kaiser.[3] He played college baseball at Aquinas College in Grand Rapids, Michigan. He signed as an amateur free agent with the Atlanta Braves in 1983, making his major league debut with them on April 12, 1986.
In his career, Assenmacher compiled a record of 61–44 with a 3.51 ERA, saving 56 games and making one career start in 884 games. He is tied with Mike Jackson for most games pitched in the 1990s (644).
Although only a .083 hitter (3-for-36), Assenmacher was a very good fielding pitcher. He recorded a .986 fielding percentage with only two errors in 146 total chances in 855.2 innings pitched.