The leader of the Conservative administration at County Hall managed to retain power during a secret ballot of the Tory group last week.
Mr Mitchell faced a challenge to his authority from cabinet member Ian Hudspeth and Thame and Chinnor councillor Nick Carter.
During the last 12 months, the Conservative-run council has announced a raft of unpopular savings, including cuts to adult social care, libraries and youth services.
All 52 Conservative county councillors were balloted and under group rules the winner needed to win the support of half.
Sources confirmed Mr Mitchell, who has been the Conservative leader since 1999 and council leader since 2001, won 28 votes.
It was just two votes more than the 26 he needed to win outright.
Mr Hudspeth, who is the cabinet member responsible for infrastructure, received 16 votes and Mr Carter had the support of eight of his colleagues.
It is understood the leadership challenge, which took place at the annual meeting of the Conservative group, is the first one Mr Mitchell has faced in recent years.
The vote comes at the end of a turbulent nine months for the council in which it has had to announce unprecedented cuts of £119m over the next four years.
We contacted all three leadership contenders this week. Both Mr Hudspeth and Mr Carter declined to comment. Mr Mitchell did not return our calls.
Tory cabinet members also remained tight-lipped on the leadership challenge.
But Conservative councillor for Didcot Ladygrove Bill Service said of the challengers: “They both believed it was time for a leadership challenge...so they put their challenge in.
“There is no bad feeling or bad blood.”
Mr Service said it was the right time for a contest to be held as it would have given any new leader time to establish themselves before the next county council election in 2013.
Although the Didcot councillor did not attend the meeting, he confirmed he voted for Mr Mitchell by proxy.
Mr Mitchell, who describes himself as “proud to be politically incorrect” on his council profile page, has been involved in several public spats.
He challenged leading authors, such as Phillip Pullman and Colin Dexter, on their opposition to the county’s plan to cut £2m from its library service budget, suggesting they had an “undeclared vested interest”.
The leader infamously branded student fees protesters who stormed County Hall as “oiks”.