Bogie, who has been at the club since 2006, and Mitchell, who joined him in 2010 were relieved of their duties by chairman Graham Wood, who told the pair at the reserves match against Chesterfield on Monday evening.
Bogie (who made 22 appearances for Newcastle United) was originally Gateshead’s assistant manager when he first came to the club and then led them to back-to-back promotions up in to the Conference top tier.
Graham Wood: "It was a difficult decision to make because Ian has taken us from the UniBond premier division to where we are today.
"The expectations at the start of the season, however, were to reach the play-offs and I believe it is still possible if we took action now.
"We have good players at the club and needed to turn the situation around before it is too late. Now is the right time to make a change at the top.
"There is still plenty to play for in both the league and the FA Trophy and bringing in a new manager with new ideas will freshen things up and help to get us back on track.
"I would like to thank Ian and Terry for their considerable efforts during their time at the club and wish them well in the future."
Former Sunderland defender and Gateshead reserve boss, Anthony Smith, has been put in charge while the permanent position is considered.