Dog has successful treatment, tail removed (3)
I believe the answer is:
cur
'dog' is the definition.
(both can mean a despicable person)
'successful treatment tail removed' is the wordplay.
'successful treatment' becomes 'cure' (eg cure for a disease).
'tail removed' means to remove the last letter.
'cure' with its last letter removed is 'CUR'.
'has' acts as a link.
(Other definitions for cur that I've seen before include "Aggressive mongrel" , "Mongrel - coward" , "Useless dog" , "Non-pedigree dog" , "Dog of low breed" .)