After a brief stint with Carolina's then-American Hockey League (AHL) 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.

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.

[11] On January 4, 2017, Sutter was awarded his second career penalty shot, converting against Mike Smith of the Arizona Coyotes.

[14] 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.

[16] He returned to Vancouver's lineup in early January before suffering another groin injury, his third in four seasons with the Canucks, on February 9, 2019, in a game versus the Calgary Flames.

[20] Sutter ultimately returned to the Canucks lineup in January 2020 and played in every subsequent game before the final month of the season was cancelled due to the COVID-19 pandemic.

[22] However, Sutter did not play in the 2021–22 NHL season due to suffering from long COVID, following his positive test result in March 2021.

He has an older brother, Merrick, who currently serves as the Rebels' senior vice president, and a younger sister, Brooke.

[27] Sutter's cousin Brett was a teammate of his with the Rebels who was drafted two years ahead of him by the Calgary Flames, and currently coaches in the American Hockey League.

In March 2021, he was one of 21 Canucks players that contracted COVID-19 and is now considered a "long-hauler" experiencing post-COVID after effects which prevent him from training.

Unlike ex-Edmonton Oilers backup goalie Alex Stalock and forward Josh Archibald, Sutter does not suffer from myocarditis, a condition that causes heart inflammation associated with COVID-19.