"exhausted mind" is correct and is a perfectly usable phrase in written English.
It is generally used to refer to a mind that has been drained of energy or enthusiasm due to too much work, stress, or emotional strain. For example, "After an intense day of exams, my exhausted mind was ready for some rest."
At 4am, I finally fell into a fitful sleep for two hours, and then the light woke me and my exhausted mind started racing again.
Malaga's players look exhausted mind.
Did he really wake up or is it my exhausted mind tricking me?
I had no idea what to do and felt incredibly overwhelmed from the moment I woke up each day to the moment I retired my exhausted mind and body back to bed.
This set of sub-themes captures the psychological and emotional impact of POCS: (i) Infertile as inferior and (ii) Exhausted mind and body.
With recession coming we're lumbering into the automatic response of exhausted minds: deflation.
In many ways, art has always provided much needed relief for our exhausted minds and worked as universal common ground especially when many of us were avoiding heated political conversations this holiday season.
During the first, exhausting, mind-numbing day of press conferences at the 2013 International Consumer Electronics Show, one phrase kept rearing its ugly, horned head: game changer.
For that reason, they advice McCain's camp to let her "be herself;" stop trying to cram hundreds of useless facts about foreign affairs and the economy into her exhausted little mind.
I could have easily called the front desk for help, but, dejected and exhausted, my mind raced through all the millions of reasons I should have never plunged into a full school year in a foreign country...I didn't know anyone, the hotel didn't want my business, and I couldn't even use an appliance without burning out a fuse!
In those days — post-apartheid, post-Live Aid — Africa seemed to have exhausted the minds and the mercy of politicians, celebrities, relief workers, missionaries and journalists.
