Mysterious giant mice all over the place (9)
I believe the answer is:
enigmatic
'mysterious' is the definition.
(I've seen this before)
'giant mice all over the place' is the wordplay.
'all over the place' indicates anagramming the letters.
'giant'+'mice'='giantmice'
'giantmice' anagrammed gives 'ENIGMATIC'.
(Other definitions for enigmatic that I've seen before include "Hard to fathom" , "Like a puzzle" , "Ambiguous or puzzling" , "Mystifying" , "Difficult to interpret" .)