After playing his junior and senior seasons of high school hockey with the Culver Military Academy, Suter joined the Dubuque Fighting Saints program in the United States Hockey League (USHL). He appeared in 18 games with the Fighting Saints in the 1981–82 season, scoring 3 goals and 7 points. He was eligible for the 1982 NHL Entry Draft, but listed at five feet, nine inches tall by the Central Scouting Bureau, was considered too small for the NHL and went undrafted. Suter established himself as one of the first star players in the USHL's junior era, improving to 39 points in 41 games in 1982–83 and leading Dubuque to the Clark Cup championship. The team's captain, he also led Dubuque to a national junior championship. He was again passed over by the NHL in the 1983 Draft, but accepted a full scholarship to play at the University of Wisconsin–Madison.