Dispose of second young dog (3,2)
I believe the answer is:
mop up
'dispose of' is the definition.
(I've seen this before)
'second young dog' is the wordplay.
'second' becomes 'mo' (both are short periods of time).
'young dog' becomes 'pup' (short for puppy).
'mo'+'pup'='MOP-UP'
(Other definitions for mop up that I've seen before include "Clear away, dispose of" , "take care of" , "Finish off a task, clean away remnants" , "Kill (enemy stragglers)" , "polish off" .)