Nyora kupfuurira kweiyi ndima - Mushure mekutamba mwaka wake wejunior uye mukuru wechikoro chepamusoro hockey neCulver Military Academy, Suter akabatana neDubuque Fighting Saints chirongwa muUnited States Hockey League (USHL). Akaonekwa mumitambo gumi nemasere neFighting Saints mumwaka wa1981-82, achihwina zvibodzwa zvitatu nemapoinzi manomwe. Akanga akakodzera nokuda kwe1982 NHL Entry Draft, asi akanyorwa pamakumbo mashanu, masendimita mapfumbamwe pakureba neCentral Scouting Bureau, akaonekwa kuti akaderera zvikuru kuNHL uye akaenda asina kunyorwa. Suter akazvisimbisa semumwe wevatambi vekutanga nyeredzi muUSHL's junior era, achivandudza kusvika pamapoinzi makumi matatu nemapfumbamwe mumitambo makumi mana nematanhatu muna 1982-83 uye achitungamira Dubuque kuenda kuhwina mukombe weClark Cup. Kaputeni wechikwata, akatungamirirawo Dubuque kunhangemutange yenyika yevaduku. Akapfuudzwa zvakare neNHL muna 1983 Draft
, asi akagamuchira bhezari rakazara rokutamba paUniversity of Wisconsin-Madison.