High school Nelson played in the
Wisconsin Interscholastic Athletic Association for the Wisconsin Rapids Lincoln High School Red Raiders at the SWCRC (South Wood County Recreation Center) in
Wisconsin Rapids, Wisconsin US.
Amateur Nelson played in the
North American Hockey League with the
Alaska Avalanche and
Johnstown Tomahawks. He was named the NAHL Defenseman of the Month for November 2012, and he played in the 2013 NAHL Top Prospects Tournament. He was named to the All-
WCHA Second Team in the 2014–15 season. 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. Nelson played alongside his brother, Josh, for the 2013–14 season.
Professional Nelson was invited to participate in a prospect camp for the
National Hockey League's
Philadelphia Flyers in the summer of 2015. 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. On June 29, 2016, Nelson signed a two-year contract extension with the Sabres. He recorded his first NHL goal on February 11, 2018, in a 5–4 loss to the
Colorado Avalanche. On May 2, 2018, Nelson re-signed with the Sabres. 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. However, Nelson later opted out of participating of the delayed
2020–21 season due to the ongoing
COVID-19 pandemic. On January 15, 2021, Nelson announced through Instagram that he was retiring from hockey after five professional seasons. ==Personal==