Branch kills American comic (8)
I believe the answer is:
offshoot
'branch' is the definition.
(I know that branch can be written as offshoot)
'kills american comic' is the wordplay.
'kills' becomes 'offs' (I've seen this in other clues).
'american comic' becomes 'hoot' (I can't explain this - if you can you should believe this answer much more).
'offs'+'hoot'='OFFSHOOT'
Can you help me to learn more?
(Other definitions for offshoot that I've seen before include "Something developing from another" , "Business subdivision, say" , "new branch" , "Development" , "Sucker" .)