Blackwood only began playing hockey at age nine. At age 12, he switched positions to goaltender and played in the Volunteer Pool Bearcats and Neebing Hawks AA house league teams before joining the Thunder Bay Kings AAA minor midget team in 2011. Blackwood was drafted by the Ontario Hockey League 's Barrie Colts in the fifth round of the 2012 OHL Priority Selection. His outstanding play during his first season with the Colts was rewarded when he was named to the 2013–14 OHL First All-Rookie Team. The following season, Blackwood was selected as a member of the OHL All-Stars for the 2014 Subway Super Series. He was also chosen to play the 2015 CHL/NHL Top Prospects Game, but was unavailable due to illness. On December 30, 2015, Blackwood signed a three-year, entry-level contract with the New Jersey Devils, which had drafted him in the 2015 NHL Entry Draft. After playing for the Devils' American Hockey League affiliate, Blackwood was assigned to the Adirondack Thunder, the Devils' ECHL affiliate, on January 1, 2018. Blackwood began the 2018–19 season with the Devils' AHL affiliate, the Binghamton Devils. He was recalled to New Jersey on December 17 after goaltender Cory Schneider was placed on injured reserve. Blackwood made his NHL debut the following night in a 7–2 loss to the Toronto Maple Leafs. He replaced starter Keith Kinkaid in the third period and saved eight of ten shots. On December 20, Blackwood made his first NHL start against the Columbus Blue Jackets, and although the Devils lost 2–1, Blackwood had an impressive performance, saving 36 of 38 shots. On December 27, Blackwood recorded his first NHL win, a 5–2 victory over the Boston Bruins, with another strong performance, making 40 saves on 42 shots. In only his third NHL start, Blackwood recorded 37 saves to earn his first shutout in a 2–0 victory over the Carolina Hurricanes on December 29. Blackwood was named a Star of the Week following this performance. Following another shutout victory on December 31 against the Vancouver Canucks, Blackwood became the first Devils rookie goaltender to post back-to-back shutouts. He also became the youngest Devils goaltender to record multiple regular season shutouts, surpassing Martin Brodeur. On January 3, 2019, Blackwood was named to the North Division roster for the 2019 American Hockey League All-Star Classic. On January 10, Blackwood was placed on injured reserve by the Devils due to a lower body injury he suffered on January 2. He returned to the Devils lineup and played his first game since January 4 in a 3–2 win over the Philadelphia Flyers on January 12.
