Rossman's father was Italian, and his mother Jewish, which led to his moniker The Jewish Bomber and a tattoo of the Star of David being etched into the calf of his right leg. He started his career in 1973, and had an impressive run in the beginning before going into some moderate 'mini-slumps' where he appeared to have a lethargic attitude toward the sport.
Things picked up, though, and he received a shot at the title held by the Argentine Victor Galindez on the undercard of Ali-Spinks rematch in September of 1978. Many thought Galindez would defeat his opponent, but Rossman opened up some cuts over Galindez' eyes and continued fighting that way until near the end of the 13th round, when the referee stopped the fight, and Rossman became world champion. Rossman would make one successful defense before his hometown Philadelphia fans in December of the same year, stopping Italian challenger Aldo Traversaro in the fifth round after busting open Aldo's forehead with a left hook. Then, in February of 1979, Rossman would fall victim to what could possibly be one of professional boxing's most embarrassing moments (at least in modern times). There he was, waiting in the ring to take on the man from whom he won the title - Galindez - in a rematch, but Galindez was not to show up. There was a feud in the challenger's camp over the fact that there should be 'neutral' judges scoring the fight. After attempts to settle things, the fight was suspended until two months later, when the two hooked up again for real in April. This time though, things were different. With the champion fretting about boxing politics, Galindez was focused on regaining the title - and he did just that. Rossman apparently broke his right hand, after which he became a one-armed fighter. The pain became worse, and unbearable to a point where Mike told his father-manager after the ninth round that he couldn't continue. Galindez was thus once again crowned champ. After the defeat, not only did Rossman no longer fight for a title, but his record seemed to go into another 'sputter.' He would fight into the early 1980's, and perhaps the biggest name he faced in post-championship status was the upstart Dwight Braxton, who stopped him in seven in May 1981.