[3] Graves had a reputation in the Nova Scotia youth hockey circuit for clumsiness, caused primarily by his comparatively tall physique.

[5] During the 2010–11 minor ice hockey season, Graves played for the South Shore Canadian Tire Mustangs, for whom he scored five goals and recorded seven assists.

[11] Prior to the 2014–15 season, Graves was again on the move in the QMJHL, traded by the Foreurs to the Quebec Remparts in exchange for Vincent Lanoue and draft picks on August 18, 2014.

He was selected to the Canadian Hockey League's Memorial Cup All-Star Team after collecting five points in five games for host club Quebec.

[13] In the 2015–16 season, Graves was assigned to the Rangers American Hockey League (AHL) affiliate, the Hartford Wolf Pack.

As a hulking defenceman with good mobility, Graves was a staple on the blueline for the Wolf Pack and represented the club at the 2016 AHL All-Star Game, winning the hardest shot contest with a 103.4 mph (166.4 km/h) slapshot.

[15] Assigned to the Wolf Pack for the final year of his rookie contract, Graves regressed with just 4 goals and 11 points in 57 games in the 2017–18 season.

[18] During the 2019–20 season, primarily playing alongside eventual Calder Memorial Trophy winner Cale Makar, Graves in a top-pairing role scored career highs in both goals and points, and lead the NHL in the plus–minus statistic at +40.

[20] Used in a top-four role, Graves was relied upon as the mainstay of the Avalanche penalty kill, finishing third in the league in short-handed time on ice.

He suffered a concussion in a game against the Columbus Blue Jackets on March 29, 2024,[25] and missed the remainder of the regular season after being placed on injured reserve on April 11.