Gifford will step down from his role with immediate effect in order to focus on “other business and personal interests”.
He will stay on at GAME until the end of March though in order to support chief executive Martyn Gibbs and the finance team.
The video games retailer has already begun the search to find a suitable successor.
“I would like to thank Mark for the significant contribution he has made to our business,” said CEO Gibbs.
“Mark has worked incredibly hard to create a solid platform, from which we are transforming GAME. All of the team would like to take this opportunity to wish him the very best for the future.”
'Leaves GAME in good shape'
“Today's news is unexpected,” wrote Liberum analyst Adam Tomlinson, who has the stock as a 'hold' with a 65p target price.
“Gifford has helped steer the business through a period of significant change, which has included developing the Events and Esports division as a key part of the group's long-term strategy, rationalising the UK Retail cost base and, more recently, securing the refinancing of the group's Spanish operations.
“We believe he leaves the group in good shape, as demonstrated by the recent strong Christmas trading update, and we are hopeful of the appointment of a replacement in due course to continue the group’s good momentum.”
Shares dived 11.6% to 41.6p in late afternoon trading on Tuesday.
--Updates for broker comment and share price--