Burroughs began his minor hockey career playing AAA bantam with the Langley Eagles. As an associate captain, Burroughs recorded 40 points in 33 games during the 2009-10 season. He then established himself with the Valley West Hawks in the BC Hockey Major Midget League where he was also named an associate captain. During the 2010–11 season, Burroughs earned a call up to the Aldergrove Kodiaks in the Provincial Junior Hockey League and Regina Pats in the Western Hockey League. He had been drafted by the Pats 47th overall in the 2010 WHL Draft. While with the Valley West Hawks, Burroughs was named a BCMML All-Star. The following season, Burroughs joined the Pats for his first full season in major junior hockey. He made his WHL season debut on September 28, 2011, against the Medicine Hat Tigers, helping the Pats win their third straight game to start off the 2011–12 season. Leading up to the 2013 NHL Entry Draft, Burroughs was ranked 206th among North American skaters. However, due to a breakout season, by April Burroughs had moved up to 133rd. On March 15, 2013, Burroughs was awarded the Charles Johnston Memorial Award as the Pats top defenceman after he led the team's defenceman in points. He was later drafted in the seventh round of the 2013 NHL Draft by the New York Islanders. On September 23, 2013, Burroughs was named captain of the Pats as a replacement for Colton Jobke who had begun his professional career. During the 2013–14 season, Burroughs suffered a concussion as the result of a hit by Brandon Wheat Kings centre Jayce Hawryluk, who was suspended two games. Burroughs was forced to sit out seven games to recover. Despite this, he recorded a new career high in goals and assists and was again awarded the Charles Johnston Memorial Award. After the Pats season had ended, Burroughs played nine games with the Islanders American Hockey League affiliate, the Bridgeport Sound Tigers, to help conclude their season. Burroughs attended the Islanders Development Camp prior to the 2014–15 season but was subsequently returned to the Pats. On January 5, 2015, Burroughs and Dryden Hunt were traded to the Medicine Hat Tigers in exchange for Connor Hobbs and future draft picks. At the time, Burroughs had recorded 22 points in 36 games for the Pats that season. While playing with the Medicine Hat Tigers in the 2015 WHL playoffs, Burroughs signed a three-year, entry-level contract with the Islanders on April 8, 2015. Burroughs contributed three points in ten games during the playoffs as the Medicine Hat Tigers lost to the Calgary Hitmen in the Conference Semi-finals.
Professional
The following season, Burroughs was assigned to the Islanders ECHL affiliate, the Missouri Mavericks, to begin the 2015–16 season and his first full season in the professional ranks. He played in 18 games for the Mavericks, recording seven points, before being recalled to the AHL. He recorded his first AHL point on January 1, 2016, with an assist on Jared Gomes' goal during a game against the Springfield Thunderbirds. On March 6, 2016, Burroughs collided with a player from the Hartford Wolf Pack, causing him to miss a month of playing time. During his rookie season, Burroughs played on the Sound Tigers second powerplay unit and on the penalty kill, leaving him to end the season with 10 points in 31 regular season games. He helped the Sound Tigers qualify for the 2016 Calder Cup playoffs, where they lost in the first round to the Toronto Marlies. After attending the Islanders training camp, Burroughs was reassigned to the Sound Tigers for the 2016–17 season. He ended the season with a new career high in goals, assists, and penalty minutes. On March 30, 2017, Burroughs was named the Sound Tigers AHL Man of the Year due to his work in the community and with charities. Burroughs recorded a spike in offense during the 2017–18 season. He ended the season with a team-leading plus-16 and a new career high in goals and points. On March 29, 2018, Burroughs was named the Sound Tigers AHL Man of the Year for the second time due to his work in the community. On July 16, 2018, Burroughs signed a two-year, two way contract extension with the Islanders. After clearing waivers, Burroughs began the 2018–19 season with the Sound Tigers. Prior to the 2018–19 season, Burroughs was named a co-captain for the Sound Tigers alongside Ben Holmstrom. Burroughs would serve as captain whenever Holmstrom was out of the lineup. On November 12, 2018, Burroughs was suspended for one game due to a high-sticking incident in a game against the Providence Bruins. A few days later on November 17, Burroughs played in his 200th AHL game.
