Part of wood I'm in I should cut down (8)
I believe the answer is:
diminish
'cut down' is the definition.
(I've seen this before)
'part of wood i'm in i should' is the wordplay.
'part of' indicates the answer is hidden within the clue.
'DIMINISH' is hidden in the letters of 'wood im in i should'.
(Other definitions for diminish that I've seen before include "Get smaller" , "make shorter" , "Become smaller or less" , "Diet" , "sink" .)