Dumba was selected with the seventh overall pick by the Minnesota Wild in the first round of the 2012 NHL entry draft, with whom he spent his first ten seasons.

Dumba previously played junior with the Red Deer Rebels and briefly for the Portland Winterhawks of the Western Hockey League (WHL).

Joining the Rebels full-time in 2010–11, Dumba scored 15 goals and 26 points and was a player whom his coach said was noticeable every time he was on the ice.

He was the youngest player invited to the selection camp for the 2012 World Junior Hockey Championship, however he failed to make the team.

Don Hay was one of several WHL coaches to praise Dumba for his enthusiasm on the ice and hard-checking style: "He's a guy who can do all aspects of the game ... he's a very dynamic player with or without the puck.

[10] Dumba was returned to the Rebels to begin the 2012–13 WHL season, in part due to a labour dispute between the NHL and its players.

[16] He played 81 out of the 82 games that season, missing only a 3–0 loss to the San Jose Sharks as a healthy scratch by coach John Torchetti.

[18] After not getting off to a good start for the Wild, new head coach Bruce Boudreau opted to scratch Dumba on October 20 against the Toronto Maple Leafs.

After that he played alongside All-Star defenseman Ryan Suter on the first defensive pairing and saw increased responsibilities and ice time.

[21] Dumba was named the 2020 King Clancy Award winner by the NHL for his efforts supporting community initiatives in Minneapolis and as a member of the Hockey Diversity Alliance.

[26] Dumba recorded his first point with the Lightning, an assist on Michael Eyssimont's goal in the first period, in a 7–4 win over the Montreal Canadiens on April 4, 2024.

[28] Dumba made his 2024 Stanley Cup playoffs debut with the Lightning on April 21 in 3–2 loss to the Florida Panthers in the opening round.