I would cut half of each clue (4)
I believe the answer is:
idea
'clue' is the definition.
('I haven't a clue' means 'I have no idea')
'i would cut half of each' is the wordplay.
'i would' becomes 'I'd'.
'cut half of' indicates taking half.
'each' cut in half is 'ea'.
'id'+'ea'='IDEA'
(Other definitions for idea that I've seen before include "Notion, image" , "Thought, conception" , "Sudden inspiration?" , "intellectual product" , "Something imagined in the mind" .)