Crushes other half's offspring (7)
I believe the answer is:
stepson
'other half's offspring' is the definition.
(son of a spouse)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for stepson that I've seen before include "Subdues" , "underfoot?" , "Child of a spouse by a former marriage" , "No pests about this relation by marriage" , "indirectly related issue" .)