[2] Growing up, Suter played for the Madison Capitols and Culver Military Academy before joining the USA Hockey's National Development Team in Ann Arbor, Michigan.

[1] Following a change to the NCAA legislature, Suter was able to enroll and play at the University of Wisconsin–Madison (UW) while remaining eligible for the 2003 NHL Entry Draft.

[6] Upon rejoining the Badgers, Suter was selected as the Western Collegiate Hockey Association (WCHA) preseason Rookie of the Year.

[7] Although Suter began the season with one goal through six games, he was given an increase in defensive responsibilities on the Badger's rookie-dominated, power-play unit.

Due to the suddenness and inconvenience of the signing, as the season had already started, Predators general manager David Poile called the Badgers head coach to apologize.

[15] As the Predators made a push for the 2006 Stanley Cup playoffs, the team traded a first-round draft pick for veteran defenseman Brendan Witt.

For the season, Suter averaged an NHL-leading 27:17 minutes of ice time as Minnesota reached the playoffs, where the team fell to the Chicago Blackhawks in the first round.

On October 19, 2018, in a 3–1 win against the Dallas Stars, Suter recorded his 500th NHL point, becoming the 11th American-born defensemen to reach the milestone.

[24] On July 28, 2021, the opening day of free agency, Suter agreed to sign a four-year, $14.6 million contract to join the Dallas Stars.

I feel it's an honor to wear the Team USA Jersey and every time I'm on the ice I play my hardest and give everything I have.

[31] In 2016, he was also selected to represent the United States at the 2016 World Cup of Hockey alongside Wild teammate, Zach Parise.

On April 19, 2019, Suter returned to the International stage for the first time in three years as he accepted an invitation to represent Team USA at the 2019 IIHF World Championship, held in Bratislava and Kosice, Slovakia.