A native of Long Branch, New Jersey, Clifton was selected 133rd overall in the 2013 NHL entry draft by the Arizona Coyotes. Clifton played prep school hockey at Christian Brothers Academy together with his brother, Tim.
Clifton began his freshman season at Quinnipiac University during the 2013-14 season. He was named to the ECAC Hockey All-Academic Team during all four seasons with the Quinnipiac Bobcats. After impressing the coaching staff, Clifton because the captain of the Bobcats during his junior season. Later that year, Clifton was named to the ECAC Hockey All-Tournament, NCAA East All-Frozen Four Team, and honored as Team ECAC Hockey Tournament Most Outstanding Player.