Like something of yours or mine that's crazy (9)

I believe the answer is:

possessed

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'that's crazy' is the definition.
(thesaurus)

I cannot understand how the remainder of the clue works.

(Other definitions for possessed that I've seen before include "Bore" , "being mad?" , "controlled by inner demons?" , "Demented" , "in need of bell, book and candle" .)

I've seen this clue in The Guardian.

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