Morrissey has represented Canada in several International tournaments, including the IIHF World U18 Championships, the Ivan Hlinka Memorial Tournament and the IIHF World U20 Championships. Morrissey was instrumental in helping the under-18 team win gold at the 2013 IIHF World U18 Championships, as well as the under-20 team at the 2015 World Junior Ice Hockey Championship. He was named to the 2015 World Junior All-Star First Team, finishing with four points and a +9 plus-minus rating.