Crazily firing without notice -- that's demeaning (5,3)
I believe the answer is:
infra dig
'demeaning' is the definition.
(I've seen this before)
'crazily firing without notice' is the wordplay.
'crazily' indicates an anagram.
'without' indicates putting letters inside ('without' can be similar in meaning to 'outside').
'notice' becomes 'ad'.
'firing' with letters rearranged gives 'infrig'.
'infrig' enclosing 'ad' is 'INFRA DIG'.
'that's' is the link.
(Other definitions for infra dig that I've seen before include "Such as one would not stoop to" , "degrading" , "Unworthy" , "Beneath oneself (from Latin)" , "Rigid fan may be lacking in dignity" .)