Hammaker was born in Carmel, California, on January 24, 1958, the son of Charles and Miyake Hammaker. Hammaker is a middle child; he has one older brother, Aldine, and one younger sister, Charlene. He is half Japanese and half German. Hammaker grew up living in many different locations due to his father's career in the United States Army. He attended Mount Vernon High School in Fairfax County, Virginia, where he played basketball, football, and baseball. After suffering a knee injury in football his sophomore year, Hammaker began focusing on basketball. He received a full basketball scholarship to East Tennessee State University (ETSU). After being talked to and convinced by the coaches at ETSU, Hammaker decided to change his focus to baseball. He attended a summer league in Alaska. From there, he was chosen as the number one draft pick to pitch for the Kansas City Royals.
Hammaker made the National League All-Star team in 1983, but did not fare well, surrendering seven earned runs in 0.2 inning pitched; and he gave up the only grand slam in All-Star Game history, to Fred Lynn.