Since there seems to be confusion about this in both languages, I figured I would clarify the distinctions in English at least: -- "to lose one's mind": to go insane -- a colloquial expression -- "to lose one's head": to lose control of oneself (can still be sane!) -- another colloquial expression -- "to lose one's spirit" (one possible loose translation of "seinen Geist verloren"): to feel defeated, to lose one's will to do something -- not really colloquial, but not common either; best thought of as a poetic phrase -- "to lose one's soul": to cease to promote or defend oneself on one's own terms, to conform to social standards one had formerly resisted (related to, but not the same as, "to sell one's soul") -- "to lose one's memory": to forget things often -- not at all colloquial
Note that probably the most literal translation of "seinen Geist verloren" would be "to lose one's ghost", which is not an expression of any kind in English (though it might get used in a story about ghosts, for instance). The similar-sounding expression, "to give up the ghost", means "to die". It is colloquial, although it has been colloquial for a very long time -- the King James Bible (early 1600s) uses the phrase!
I imagine that there are a similar number of German expressions along the same lines. Would any fluent German speakers like to give examples?