Barrasso had originally intended to play for the 1984 U.S. Olympic team in Sarajevo, but chose to begin his professional career instead and left the team in September 1983 to sign with the Sabres. He made his debut for Team USA at the 1984 Canada Cup, at the age of 19. He also played in the 1983 World Junior Championships, the 1986 World Ice Hockey Championships and the 1987 Canada Cup.