Mongrel dog — what it wags cut short (7)
I believe the answer is:
curtail
'cut short' is the definition.
(synonyms)
'mongrel dog' is the wordplay.
'mongrel' becomes 'cur' (synonyms).
'dog' becomes 'tail' (synonyms).
'cur'+'tail'='CURTAIL'
'what it wags' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
(Other definitions for curtail that I've seen before include "Cut short like canine appendage" , "Reduce in extent" , "Shorten, abridge" , "Abbreviate" , "make shorter" .)