Musselman graduated from Central Regional High School in Bayville, New Jersey and Harvard University. In 1984, he played collegiate summer baseball in the Cape Cod Baseball League for the Yarmouth-Dennis Red Sox.
He was drafted in the sixth round of the 1985 Major League Baseball draft by the Blue Jays. His best season in the majors was 1987, when he appeared in 68 games for Toronto, posting a 12–5 record with a 4.15 ERA at 54 strikeouts in 89 innings of work.
On July 31, 1989, he was traded by the Toronto Blue Jays with minor leaguer Mike Brady to the New York Mets for Mookie Wilson. He appeared in 20 games for the Mets in 1989, posting a 3–2 record with a 3.08 ERA.

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