Anaesthetise small dog biting tot, else in trouble (3,2,5)
I believe the answer is:
put to sleep
'anaesthetise' is the definition.
('put to sleep' can be a synonym of 'anaesthetize')
'small dog biting tot else in trouble' is the wordplay.
'small dog' becomes 'pup' (I've seen this before).
'biting' is an insertion indicator (I've seen this in other clues).
'in trouble' indicates an anagram.
'tot'+'else'='totelse'
'totelse' is an anagram of 'ttoslee'.
'pup' going around 'ttoslee' is 'PUT TO SLEEP'.
(Another definition for put to sleep that I've seen is " Kill humanely".)