After a brief stint with Carolina's then-American Hockey League affiliate, the Albany River Rats, at the end of his 2007–08 WHL season, Sutter debuted in the NHL with the Hurricanes in 2008–09. He scored his first NHL goal on October 23, 2008, against Marc-André Fleury of the Pittsburgh Penguins. The next game, on October 25, Sutter suffered a concussion after a collision with Doug Weight of the New York Islanders. Sutter had his head down as he was leaning forward for a loose puck in the neutral zone when Weight caught him with his shoulder. Although the hit was ruled as legal and Weight was not assessed any penalty, it re-sparked the debate in the NHL on head shots. Sutter returned to the line-up after missing eight games. On July 12, 2011, Sutter signed a three-year, $6.2 million contract extension with Carolina.
Pittsburgh Penguins
On June 22, 2012, Sutter was traded to the Pittsburgh Penguins in exchange for Jordan Staal. On March 12, 2013, in a game against the Boston Bruins, he scored two goals 3:24 apart in the third period that led to a 3–2 comeback victory for Pittsburgh. On August 5, 2014, the Penguins announced they had re-signed Sutter to a two-year, $6.6 million contract extension.
Vancouver Canucks
On July 28, 2015, Sutter was traded to the Vancouver Canucks in exchange for Nick Bonino, Adam Clendening and a second-round pick in 2016. On August 4, 2015, the Canucks announced they had signed Sutter to a five-year, $21.875 million contract extension. Sutter played 16 games in the 2015–16 season before it was revealed he required sports hernia surgery. He missed 33 games before returning to the Canucks lineup on January 26, 2016. However, on February 9, his fourth game back since the surgery, he suffered a broken jaw in a game against the Colorado Avalanche that sidelined him for the remainder of the season. Sutter scored 5 goals and 4 assists for 9 points in 20 games for the Canucks in an injury-plagued 2015–16 season. In August 2016, the Canucks announced Sutter had switched from number 21 to 20 to let new Canucks acquisition Loui Eriksson wear number 21. On January 4, 2017, Sutter was awarded his second career penalty shot, converting against Mike Smith of the Arizona Coyotes. On November 24, 2017, Sutter suffered a groin injury in a 3–2 loss to the New Jersey Devils. After missing 21 games, Sutter returned to the lineup on January 14, 2018, scoring the overtime-winning goal in a 3–2 win over the Minnesota Wild. On October 29, 2018, Sutter suffered a separated shoulder in a game against the Minnesota Wild. He was expected to miss four-to-six weeks.
International play
Sutter, who has dual citizenship of both the United States and Canada, elected to play for Canada in international competition. Sutter represented Canada extensively during his junior career at the under-18 and under-20 levels. He competed in two IIHF World U18 Championships in 2006 and 2007, losing the bronze medal game in both tournaments. Shortly after being drafted into the NHL in the summer of 2007, Sutter was chosen to represent Canada at the 2007 Super Series, an eight-game showdown between Canada and Russia's under-20 teams, where father Brent Sutter was head coach. Playing Game 7 in his hometown of Red Deer, Alberta, he scored a goal and was named player of the game. Coincidentally, the match also marked the last junior game Brent coached in Red Deer, where he had previously just completed a seven-year coaching career with the Red Deer Rebels. Sutter made his second under-20 appearance for Canada at the 2008 World Junior Championships in the Czech Republic, where he helped Canada win gold, overcoming Sweden 3–2 in overtime.
Family
Sutter is part of the venerable Sutter hockey family. He is the son of Brent Sutter, who coached him in junior with the Red Deer Rebels and Team Canada at the 2007 Super Series; Brent is a former head coach of the Calgary Flames. He has an older brother, Merrick who currently serves as the Rebels Senior Vice President and a younger sister, Brooke. His cousin Brett was a teammate of his with the Rebels who was drafted two years ahead of him by the Calgary Flames, was the captain of the Charlotte Checkers—the Carolina Hurricanes' AHL affiliate—and currently plays in the Los Angeles Kings organization. Another cousin, Brody, played for the WHL's Lethbridge Hurricanes and was drafted 193rd overall by Carolina in the 2011 draft. Brody currently plays with Vaasan Sport of the Finnish Liiga. As a result of his father's career, Brandon grew up in Huntington, New York, and Chicago, Illinois, before his family settled in Red Deer, Alberta, following Brent's purchase of the Red Deer Rebels organization.