[1] Mitchell was selected 57th overall by the Chicago Blackhawks in the 2017 NHL Entry Draft, but committed to play college ice hockey at the University of Denver starting in the 2017–18 season.

Mitchell considered going pro and signing with the Blackhawks prior to the 2019–20 season, but elected to stay with Denver, where he was named captain.

[9] Mitchell logged his first NHL point on January 22, 2021 against the Detroit Red Wings with an assist on a goal by Calvin de Haan.

Although not a lineup regular, Mitchell stayed with the NHL club for the majority of his rookie season, finishing with three goals and four assists in 39 games.

In 2021–22 Mitchell did not find the same NHL success that he found in his rookie season, as he spent the majority of the year with the Blackhawks' AHL affiliate, the Rockford IceHogs.

On June 26, 2023, as an impending RFA, Mitchell was traded by the Blackhawks to the Boston Bruins with Alec Regula in exchange for Taylor Hall and Nick Foligno, reuniting him with his head coach from Denver, Jim Montgomery.

As a pending free agent, Mitchell opted to continue his tenure with the Bruins by signing a one-year, two-way contract extension on June 23, 2024.