Giant mice can be mysterious (9)
I believe the answer is:
enigmatic
'mysterious' is the definition.
(I've seen this before)
'giant mice can be' is the wordplay.
'can be' is an anagram indicator.
'giant'+'mice'='giantmice'
'giantmice' anagrammed gives 'ENIGMATIC'.
(Other definitions for enigmatic that I've seen before include "Ambiguous or puzzling" , "Obscure, puzzling" , "Hard to fathom" , "Like a puzzle" , "Difficult to interpret" .)