Following a promising rookie campaign on the blueline, posting 21 points in 62 games with the Generals, in the 2015–16 season, Stillman was selected in the 2016 NHL entry draft by the Florida Panthers, 114th overall.
During his final junior season in 2017–18, Stillman was traded by the Generals to contending club, the Hamilton Bulldogs in exchange for future draft picks on December 28, 2017.
After attending the Panthers 2018 training camp, Stillman was assigned to begin his professional career with AHL affiliate, the Springfield Thunderbirds, for the 2018–19 season.
[10] Approaching the 2022–23 season, Stillman was traded by the Blackhawks to the Vancouver Canucks in exchange for Jason Dickinson and a second-round pick in the 2024 NHL entry draft on October 7, 2022.
[12] After parts of two seasons within the Sabres organization, Stillman left the club as a free agent and was signed to a one-year, two-way contract with the Carolina Hurricanes on July 3, 2024.