Dogged mongrel's first to get docked (9)
I believe the answer is:
curtailed
'docked' is the definition.
(thesaurus)
'dogged mongrel's first' is the wordplay.
'dogged' becomes 'tailed' ('tail' can be a synonym of 'dog').
'mongrel' becomes 'cur' ('cur' can be a synonym of 'mongrel').
'first' is a charade indicator (letters next to each other).
'tailed' put after 'cur' is 'CURTAILED'.
'to get' acts as a link.
(Other definitions for curtailed that I've seen before include "docked" , "limited" , "Made short" , "Clipped" , "Cut short" .)