[4] Puljujärvi played in the 2011 Quebec International Pee-Wee Hockey Tournament with the Finland Selects youth team.

[5] Puljujärvi moved to Oulu alone at the age of 13 and started to play in the local hockey club Kärpät.

In the following season, Puljujärvi moved up to the U18 juniors and scored 51 points, which earned him the Heino Pulli award given to the U18 rookie of the year.

[12] The next time Puljujärvi appeared in Kärpät's roster was in the Champions Hockey League match on 5 September, against Germany's Kölner Haie.

[14] He was immediately named to the Kärpät's first team next to Nicolas Deschamps and Mika Pyörälä and Puljujärvi got 11.53 minutes of ice time.

[20] In January 2016, the NHL scouting office listed Puljujärvi in second place in the draft ranking among players playing in Europe.

98 with the team, making him the first NHL player to do so since 1985, when Brian Lawton wore the number in a regular season game.

Puljujärvi remained in a rather small role in the Oilers and at the end of the autumn was dropped from the squad, until in January 2017 the club sent him to the lineup of the AHL affiliate Bakersfield Condors.

[35] On 20 January 2018, Puljujärvi registered a career-high three-point game, recording one goal and two assists against the Vancouver Canucks.

[41] However, he continued in Kärpät, where Puljujärvi formed an effective number one line together with Juho Lammikko and Mika Pyörälä.

[42] He led the team in points and goals and shared the top spot in assists with Juho Lammikko.

[44] In the Champions Hockey League, Puljujärvi was Kärpät's best scorer with Michal Krištof and Jakub Krejčík with four points.

[48] Puljujärvi played 16 matches for Kärpät, scoring 12 points, until the Oilers invited him to their organization in December.

[49] As a restricted free agent following the 2021–22 season, Puljujärvi avoided arbitration with the Oilers after re-signing to a one-year, $3 million contract extension on 26 July 2022.

[1] For the 2023–24 NHL season, Puljujärvi signed a professional tryout (PTO) contract with the Pittsburgh Penguins.

[58] Regaining his conditioning and having posted nine points through 13 games with Wilkes-Barre, on 4 February 2024, Puljujärvi was signed to a two-year, $1.6 million deal with Pittsburgh following the NHL All-Star break.

[61] On 8 February 2025, the Penguins organization placed Puljujärvi on unconditional waivers with the purpose of mutually terminating the remainder of his contract.

[63] On 10 February 2025, Puljujärvi opted to continue his career in North America, signing a professional tryout contract to remain in the AHL with the Charlotte Checkers, affiliate to the Florida Panthers.

[64] Puljujärvi helped team Finland win the silver medal at the 2015 IIHF World U18 Championships in Switzerland.

In the Urheilulehti article written by Ilkka Palomäki, it is pointed out that it is typical for Puljujärvi to take disproportionately large risks when trying to deke the opponent.

[71] Sportsnet's journalist Andrew Berkshire, who specializes in statistical analysis, also emphasized Puljujärvi's play in the neutral zone.

[73][74] Canadian The Sports Network expert Craig Button compared Puljujärvi to Blake Wheeler, but has since come to consider him more of a Jarome Iginla-like player.