Cassidy was a defenceman who played in the Ontario Hockey League (OHL) with the Ottawa 67's from 1982 to 1985, and he was selected by the Chicago Black Hawks of the National Hockey League (NHL) in the 1983 NHL Entry Draft, selected in the first round, 18th overall. Cassidy's best OHL season was in 1982–83, when he registered 25 goals and 86 assists for 111 points. He won the Memorial Cup under coach Brian Kilrea in 1984 scoring 12 points. At age 19, he made his NHL debut with the Black Hawks in March 1984. From 1984 to 1988, he had three knee surgeries, including major reconstruction of his ACL.