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