2009-10: Joseph Blandisi played for the Toronto Red Wings U16 team in the Greater Toronto Hockey League.
2010-11: Blandisi skated in seven Junior A games with the Vaughan Vipers and was the top scorer for the Vaughan Kings midget major team. He scored 2 goals and had 14 penalty minutes in his brief tenure with the OJHL's Vipers. In 41games with the Kings he scored 51 goals with 41 assists. Blandisi was selected by Owen Sound in the third round (61st overall) of the 2011 OHL Priority Draft.
2011-12: Blandisi saw significant ice time in a lower line role and also played on the wing at times for the Attack as a 17-year-old OHL rookie. In 68 games he scored 17 goals with 14 assists and was plus-four with 72 penalty minutes. Blandisi got off to a fast start offensively, posting 20 points in his first 33 games but had just two goals after January as he played more of a defensive role. In the five-game playoff series with Kitchener he had 1 assist and was minus-three with 8 penalty minutes. Ranked 195th amongst North American skaters in Central Scouting's mid-term rankings but not among the 210 players in the final rankings, Blandisi was selected by Colorado in the sixth round (162nd overall) of the 2012 NHL Draft.
2012-13: Blandisi went from playoff-bound Owen Sound to the last-place Ottawa 67's as part of the January trade that sent Senators' 2012 first round pick Cody Ceci to the Attack. In 37 games with Owen Sound he scored 7 goals with 18 assists and was +10 with 49 penalty minutes. He was one of Ottawa's leading scorers after the trade – scoring 8 goals with 18 assists in 26 games and was -14 with 68 penalty minutes. Ottawa was fifth in the East Division and had the OHL's worst record.