Nelson joined the NCAA's Minnesota State Mavericks in 2013 and played three seasons at the school.[3] He was named to the All-WCHA Second Team in the 2014–15 season.[1] In the 2015–16 season, he was named the conference's Defensive Player of the Year while being named to the All-WCHA First Team.[4]
Nelson played alongside his brother, Josh, for the 2013–14 season.[5]
Nelson was signed to an entry-level professional contract by the NHL's Buffalo Sabres on March 22, 2016.[6] He made his NHL debut with the team on March 26, tallying his first NHL point on an assist in the first period of a game against the Winnipeg Jets.[7]
On June 29, 2016, Nelson signed a two-year contract extension with the Sabres.[8] He recorded his first NHL goal on February 11, 2018, in a 5–4 loss to the Colorado Avalanche.[9] On May 2, 2018, Nelson re-signed with the Sabres.[10]
As a free agent, Nelson initially returned for a sixth season within the Sabres organization by agreeing to a one-year, two-way contract extension on October 22, 2020.[11] However, Nelson later opted out of participating of the delayed 2020–21 season due to the ongoing COVID-19 pandemic.[12]
On January 15, 2021, Nelson announced through Instagram that he was retiring from hockey after five professional seasons.[13]