[3] In the 2011–12 season, Demko played with the Omaha Lancers of the United States Hockey League (USHL).

[5] Demko played for the Boston College Eagles of Hockey East from 2013–2016, serving as the primary starting goaltender for all three seasons.

During his college career, he earned an impressive 62–26–10 record, with a .928 save percentage, 2.08 goals allowed average and 13 shutouts.

He also helped the Eagles earn their 5th consecutive title in the prestigious Beanpot tournament played between Boston's elite hockey universities.

He also earned a number of other accolades, making the AHCA All-American Second Team, the Hockey East First All-Star team, and finally was named Co-Player of the Year by Hockey East, alongside UMass Lowell's goaltender Kevin Boyle[10][11] Forgoing his senior year at Boston College, Demko signed a three-year entry-level contract with the Canucks on April 20, 2016.

[12] The Canucks assigned Demko to their American Hockey League (AHL) affiliate, the Utica Comets for the 2016–17 season.

[17] On March 31, 2018, Demko made his NHL debut for the Canucks, stopping 26 shots en route to a 5–4 overtime victory over the Columbus Blue Jackets.

[22] Beginning on February 25, 2020 against the Montreal Canadiens, Demko would start 7 of the final 8 games of the season, going 3–4–0 and posting a .906 save percentage.

[25] In his first three playoff starts, Demko made 123 stops on 125 shots for a remarkable .984 save percentage, nearly leading the Canucks to a 7 game series upset of the top seeded Golden Knights.

[26] The shutout would be the first game in an 8–1–0 run by Demko to start the month of March, in which he posted a .950 save percentage and a 1.74 goals against average.

Demko would get his first appearance at a senior men's international tournament at the 2019 IIHF World Championship as a backup to Cory Schneider.