Suter was the third member of his family to play defense for the Wisconsin Badgers, following brothers John and Bob. He appeared in 34 games in 1983–84, scoring 22 points. Ian McKenzie, coordinator of scouting for the Calgary Flames, noticed Suter's play at Wisconsin and that he had added over two inches of height, which Central Scouting had failed to update in its record on him. The Flames picked Suter with their ninth round selection, 180th overall, in the 1984 Draft. Suter, who had been working in a beer factory, was initially disappointed at his selection. He was in his last year of draft eligibility and was hoping to follow other college players who signed lucrative contracts as free agents after going unselected. Following his sophomore season of 1984–85, in which he recorded 51 points in 39 games for Wisconsin, Suter left Wisconsin to turn professional.