Abbott spent his collegiate career playing for the Maine Black Bears in the a NCAA Men's Division IHockey East conference. In his senior year, Abbott's outstanding play was rewarded with a unanimous selection to the 2011–12 Hockey East First-Team All-Stars, as well as being named the 2011–12 Athletic Republic Player of the Year. Abbott was assigned to the Toronto Marlies on September 15, 2012, to participate in the upcoming AHL training camp. He made his NHL debut on October 5, 2013, in the Maple Leafs home opener against the Ottawa Senators. In the 2014–15 season, on February 26, 2015, Abbott was traded to the Chicago Blackhawks in exchange for T. J. Brennan. He was reassigned to their AHL affiliate, the Rockford IceHogs, where he remained for the duration of the season, recapturing his offense to produce 21 points in 19 games. As an impending free agent, Abbott signed his first contract abroad in agreeing to a one-year contract with Swedish club Frölunda HC of the SHL on June 16, 2015. He had a very successful season in Sweden, including winning the Swedish national championship and the Champions Hockey League. In 51 SHL contests, Abbott tallied 14 goals and 22 assists, while scoring eight goals and five assists in eleven CHL appearances. On July 1, 2016, he returned to the Chicago Blackhawks as a free agent on a one-year, two-way deal. Abbott began the 2016–17 season, in his second stint with the Rockford IceHogs. Amongst the IceHogs scoring leaders, Abbott was recalled and made his debut for Chicago, his second NHL appearance, in a 4–3 victory over the Buffalo Sabres on January 5, 2017. He was returned to Rockford following the game and proceeded to collect 35 points in 53 games. At the NHL trade deadline, Abbott was dealt by the Blackhawks, along with Sam Carrick to the Anaheim Ducks in exchange for Kenton Helgesen and a 7th round pick in 2019 on March 1, 2017. As a free agent from the Ducks, Abbott opted to extend his tenure with affiliate, the San Diego Gulls, signing a one-year AHL contract on September 25, 2017. In the 2017–18 season, while leading the Gulls in scoring with 20 points in 17 games, Abbott was traded to the Binghamton Devils in exchange for future considerations on December 8, 2017. He initially refused to report to Binghamton and was suspended without pay by the team. On December 22, he signed for the remainder of the season with Swiss-based club, EHC Kloten in the National League. Helping Kloten avoid relegation, Abbott left as a free agent and returned for a second tenure in the SHL, agreeing to terms with Mora IK on September 17, 2018. In the 2018–19 season, Abbott led Mora's offense, registering 29 assists and 36 points in 42 regular season games. He was unable to prevent Mora from relegation, with only 3 points in 5 games against bitter rivals Leksands IF. On June 26, 2019, Abbott left Mora to continue in the SHL, agreeing to a one-year contract with the newly promoted Leksands.
