... so is mine after learning Polish :)
What does it mean? 'He is too tired to think' or what?
Yes, something like that.
Why not his brain?
We differentiate umysł=mind and mózg=brain.
They both mean He is too tired to think, but OK - I understand that the translation should be as precise as possible.
More appropriate to say "he is tired and cannot think.
We say at times : His mind is extremely exhausted
And that seems... quite extreme. Definitely more than just "very tired" ;)
I could see this being said in Poland. Ive found that certain phrases like this get a little poetic or less straightforward.