It's not an idiom I know anyway, so it makes no difference -- I'd probably render that as "he's got a screw loose", and "he's missing a few cups" is certainly more natural English.

Apparently there's also an insulting expression "to be a cloudy/murky cup" (presumably referring to the contents rather than the container itself): if you call someone "eine trübe Tasse", you're saying he's stupid, feeble or useless.

Or you can accuse him of having a crack in his cup.
https://de.wikipedia.org/wiki/Nicht_alle_Tassen_im_Schrank_haben