Cut page or chapter up (4)
I believe the answer is:
crop
'cut' is the definition.
(cropping is a kind of cutting)
'page or chapter up' is the wordplay.
'page' becomes 'p'.
'chapter' becomes 'c'.
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'p'+'or'+'c'='porc'
'porc' reversed gives 'CROP'.
(Other definitions for crop that I've seen before include "Dock" , "Graze" , "Short haircut" , "Hairstyle; gullet pouch" , "The handle of a whip, or part of bird's neck" .)