Joe Cirella was selected fifth overall in the 1981 NHL Entry Draft by the Colorado Rockies. He joined the OHL's Oshawa Generals at the age of 17, playing there for three years. Between his second and third years in junior, Cirella was called by the Rockies for full-time duty at the age of 18 in 1981-82. He played in 65 games, scoring seven goals and 19 points. The following year, he was returned to the Generals for the 1982-83 season, which he called the shock of his life at the time. It took him a while to get over the demotion, but once he did, Cirella was one of the premier defensemen in the OHL. Cirella notched 68 points in 56 games as the Generals captured the Ontario championship. They represented the OHL at the Memorial Cup, where they lost 8-3 to Portland in the championship game.
By 1982-83, the Colorado Rockies franchise had moved to New Jersey and been re-named the Devils. Cirella played two games with the team that year, but it was the following season when he dressed for 79 games, scoring eleven goals and 44 points, which was a career high. Cirella played another five years in New Jersey before signing with the Quebec Nordiques in 1989-90. After a little over a season in Quebec, he was traded to the New York Rangers where he played the next three years of his career.
IN 1993-94, Cirella joined the Florida Panthers for two years before finishing his NHL career in an Ottawa Senators uniform in 1995-96, having suited up for six games. He played one more year of professional hockey with the Cologne Sharks of the German Elite League before retiring after the 1996-97 season.
Cirella played in 828 games, scoring 64 goals and 275 points with 1,448 minutes in penalties.