[1] Asplund made his Swedish Hockey League debut playing with Färjestad BK during the 2014–15 SHL season.

[2] Following his fourth SHL season, Asplund signed a three-year, entry-level contract with the Buffalo Sabres on 23 May 2018.

[3] On 16 September 2020, with the North American set to be delayed due to the COVID-19 pandemic, Asplund remained in Sweden to begin playing on loan from the Sabres with Västerås IK of the HockeyAllsvenskan.

[4] He recorded 9 points through 14 games in the second tier Allsvenskan before ending his loan and returning to the Sabres.

[5] Leaving the Predators after failing to receive a qualifying offer, Asplund was signed as a free agent on a one-year, two-way contract with the Florida Panthers on 5 July 2023.