Cirelli started his junior career with the Oshawa Generals of the Ontario Hockey League. Cirelli went undrafted in the OHL draft, and would end up making the team as a walk-on. Cirelli scored the game-winning goal in overtime against the Kelowna Rockets in the 2015 Memorial Cup. On June 27, 2015, the Tampa Bay Lightning selected Cirelli 72nd overall in the 3rd round of the 2015 NHL Entry Draft. On January 28, 2016, Cirelli was named as captain of the Generals. On May 19, 2016, the Lightning signed Cirelli to a three-year entry level contract. On January 9, 2017, Cirelli was traded by the Oshawa Generals to the Erie Otters. Cirelli would go on to help the Otters capture the J. Ross Robertson Cup, which is awarded to the champion of the OHL. However, the Otters would ultimately fall in the championship game to the Memorial Cup Tournament host Windsor Spitfires in the 2017 Memorial Cup.
Professional
On March 1, 2018, Cirelli was recalled by the Tampa Bay Lightning from the Syracuse Crunch of the American Hockey League. Prior to his recall Cirelli was enjoying a productive rookie season with the Crunch. He had appeared in 51 games where he had 14-goals and 37 points. Cirelli would make his NHL debut that night against the Dallas Stars at American Airlines Center. Cirelli recorded his first career NHL goal and assist in the game, which resulted in a 5–4 overtime win. Cirelli also became only the fourth player in Lightning history to have a multiple point game in their NHL debut. On April 12, 2018, Cirelli made his NHL Stanley Cup Playoff debut in a 5–2 Lightning victory over the visitingNew Jersey Devils. On April 21, 2018, Cirelli recorded his first career playoff assist and point in a 3–1 Lightning series clinching win over the New Jersey Devils. On May 2, 2018, he recorded his first career playoff goal in a 4–1 win over the Boston Bruins.
International play
On April 29, 2019, Cirelli was selected to make his full international debut after he was named to the Team Canada roster for the 2019 IIHF World Championship, held in Slovakia. He helped Canada progress through to the playoff rounds before losing the final to Finland to finish with the Silver Medal on May 26, 2019. Cirelli finished the tournament posting 3 goals and 4 points in 10 games.
