While being raised in Rochester, Dugan played Tier 1 youth hockey for the Rochester Monarchs program before entering high school.[5] Dugan spent two seasons at McQuaid Jesuit High School where his father served as an English teacher.[3] Although he was offered opportunities within the Ontario Hockey League, Dugan chose to maintain his NCAA eligibility.[6] During his junior year at McQuaid, he helped them win the Division 1 state championship after he tallied 65 points through 24 games. As a result of his play, Dugan was named the 2015 New York High School Player of the Year.[5] Following the 2014–15 season, Dugan transferred to the Northwood School in Lake Placid, New York, where he was named to the United States High School All USA Hockey Third Team.[3] In his senior year, Dugan committed to play for Providence College following a season in the United States Hockey League.[7]
On May 11, 2020, Dugan concluded his collegiate career as he was signed by the Vegas Golden Knights to a two-year, entry-level contract.[11]
Released as a free agent from the Golden Knights following his entry-level contract, Dugan agreed to a one-year, two-way contract with the New Jersey Devils on July 13, 2022.[12] Assigned to begin the 2022-23 season in the AHL with affiliate, the Utica Comets, Dugan posted 11 goals and 27 points in 51 regular season games. On March 10, 2023, Dugan was traded by the Devils to the Carolina Hurricanes in exchange for Zack Hayes.[13]