Mitchell made his debut for Newcastle United's reserve team in January 2011 while still at school.[3] He spent time on loan at Workington during the second half of the 2012–13 season,[3] and returned to the club for a second loan spell in August 2013.[7]
He was released by Newcastle in June 2014, signing immediately for Derby County.[8][9] He said he was looking forward to working with Derby's goalkeeping coach Eric Steele.[10] He made his professional debut on 9 January 2016 in the FA Cup against his hometown club Hartlepool United.[11]
On 21 March, Mitchell was named in the Football League Team of the Week for his performance against Plymouth Argyle two days earlier when he made a number of saves, mostly notably from Graham Carey and Gregg Wylde, keeping a clean sheet to help Luton earn a 1–0 away win.[14][15] Following an injury to Lee Grant, Derby recalled Mitchell early from his loan on 5 April.[16]
He moved on loan to Oxford United in August 2018 as cover for the injured Simon Eastwood.[17] He kept a clean sheet on his first-team debut (a 2–0 home victory over Coventry City in the EFL Cup[18]) and saved a penalty on his league debut, a 4–1 away defeat at Portsmouth.[19] Mitchell finished the loan with 15 appearances, with 10 of those appearances coming in the league.[20]
On 21 January 2022, Mitchell joined League One club Doncaster Rovers on an eighteen-month deal.[30][31] Mitchell was released at the end of the 2022–23 season.[32]
In November 2023 he signed for Harrogate Town.[33] He was released by Harrogate at the end of the 2023–24 season.[34]