In addition to his NHL career, Stevens represented Canada in several international ice hockey competitions. He attended summer camp with Team Canada prior to the 1983 World Junior Championships, but because of his commitment to the Capitals, he was unable to join the team. His first experience with the senior team was at the 1983 World Ice Hockey Championships, where he won a bronze medal. The following year he made the Canadian team for the 1984 Canada Cup, but he did not play. During the 1985 World Ice Hockey Championships, he scored a goal and added two assists as Canada finished with a silver medal. He played only two games during the 1987 tournament; Canada finished in fourth place. Two years later, he scored two goals as Canada once again won the silver medal. During the tournament, he suffered a serious cut when Börje Salming's skate sliced his face; he would receive 88 stitches for the wound. He finally won international gold with Canada during the 1991 Canada Cup. Five years later, he played in the 1996 World Cup of Hockey, the successor to the Canada Cup. Finishing with two assists, Stevens won the silver medal; Canada finished in second place after giving up four goals in the final four minutes of the championship game against the American team.