Murray played forward during much of his youth but switched to defence while playing midget AAA hockey for the Moncton Flyers.
QMJHL
Murray went undrafted in his QMJHL draft year but was later signed by Patrick Roy to join the Quebec Remparts for the 2010-2011 season. At the beginning of training camp, Roy traded Murray to Acadie–Bathurst Titan for a 9th round pick in the 2011 QMJHL draft. Roy stated he didn't have room for him on his blueline but felt he was good enough to play in the league. He played most of his first season with the Titan as a bottom 6 forward. He earned a regular spot in the top 4 defence for the Titan in his second season. At the 2012 QMJHL entry draft, Murray was traded to the Drummondville Voltigeurs. He enjoyed a break-out season with Drummondville in 2012-13 as a top pair defenceman registering 56 points in 64 games, good enough for 4th in the QMJHL among defencemen.
UNB Varsity Reds
Murray committed to UNB for the 2013-14 season. In his first season with Reds, he earned All-Canadian Rookie team honours. Murray continued that success into his second season at UNB where he helped guide the Reds to the AUS championship followed by the nationalchampionship game ultimately falling to the Alberta Golden Bears 6-3. He was also named to the first All-Canadian team and was nominated for the defenceman of the year award. Once again, he built upon his previous season's success in his third season. At Christmas he was selected as a CIS All-Star to play a two-game series versus Team Canada. In March he capturing a national championship defeating St.F X in the final game. He was once again named to the first All-Canadian team and named U Sports Defenceman of the Year leading all AUS defencemen in scoring tying for fifth in the country. At the conclusion of the season, Murray was one of four male CIS athletes nominated for the BLG award which is awarded to the top male athlete in CanadianUniversity Sports. His senior year at UNB proved to be his most successful. He once again led all AUS defencemen in scoring, this time with 40 points in 30 games which was good enough to lead the country. That point total was tied for seventh in U Sports for all skaters. Jordan also returned as member of the USports All-Star team that played a two-game series against Team Canada in mid-December. For the third year in a row, he was named to the first All-Canadian team and captured back-to-back U Sports Defenceman of the Year honours. He helped UNB capture the national championship for the second consecutive year.
Professional
On April 5, 2017, Murray signed an ATO contract with the Binghamton Senators. On April 12, 2017, in his third game, he scored a goal and added an assist against Rochester for his first point and goal as a pro. On April 25, 2017, Murray signed a two-year AHL deal with the Belleville Senators. In the 2017–18 season, on November 11, 2017, Murray recorded his first professional and first Belleville Senators Hat-trick.
