Perunovich attended Hibbing High School from 2014 to 2017, during which he played three seasons of prep school hockey and tennis. While playing for the Hibbing High School Bluejackets Bantam A team in 2014, he was drafted by the Cedar Rapids RoughRiders of the United States Hockey League (USHL). He opted to continue to play for Hibbing High School, where he led the team to a 37–10–5 record and was named a finalist for Bantam Player Of the Year.

In 2015, Perunovich committed to play Division 1 hockey for the University of Minnesota–Duluth Bulldogs starting in the 2017–18 season. Team USA head coach Derek Plante, who had helped Duluth recruit Perunovich, called him a "very crafty, a smart hockey player." The 2015–16 season proved to be one of his best both on the ice and tennis court. As a sophomore and junior, Perunovich and Jake Jolowsky won the Section 7A doubles title and qualified for the Minnesota high school boys tennis state tournament for a third consecutive season. Overall, he won 80 percent of his matches and was named the Mesabi Daily News, Hibbing Daily Tribune, and Grand Rapids Herald Review Tennis Player of the Year. In January 2016, Perunovich joined the U.S. National Under-18 Team for two games against St. Cloud State. After his senior year, Perunovich then played one season with the Cedar Rapids RoughRiders during which he struggled being away from home and recorded the worst plus-minus in the league.
Perunovich played for the University of Minnesota–Duluth Bulldogs from 2017 to 2020, where he enrolled in the College of Liberal Arts, majoring in communications. Perunovich played 42 games for the Bulldogs during the 2017–18 season and recorded his first collegiate goal in a 4–3 loss to Michigan Tech on October 7, 2017. Perunovich ended his freshman season with 36 points, tying fourth nationally among all defenseman and third for freshman. As a result of his outstanding play, Perunovich was named an AHCA East First-Team All-American, NCHC First All-Conference Team, NCHC All-Rookie team, All-Tournament Team, NCHC Offensive Defenseman of the Year, and NCHC Rookie of the Year. He was the first Minnesota–Duluth Bulldog to be named Rookie of the Year and Offensive Defenseman of the Year and set a new Bulldogs record for most points by a freshman defenceman. His prolific freshman season helped the Bulldogs win the NCAA National Championship title and he was named to the NCAA Frozen Four All–Tournament Team. He was also the first NCHC player to be awarded the Tim Taylor Award as men's Division I National Rookie of the Year.

Perunovich's strong play during his rookie season earned him a midterm ranking by the NHL Central Scouting Bureau, for an eventual final rank of 102nd overall for North American Skate…

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Perunovich has represented the United States at various international tournaments at the junior level. In 2015, he was invited to participate with Team USA at the 2015 Ivan Hlinka Memorial Tournament, where they finished in fifth place.

In December 2017, Perunovich was selected for the United States men's national junior ice hockey team preliminary roster prior to the 2018 World Junior Ice Hockey Championships. After making the final cut, he scored one goal and two assists during the tournament to help Team USA win a bronze medal. His only goal of the tournament came during the first outdoor World Juniors game to eliminate a two-goal deficit and beat Team Canada 4–3.