WordNet sense 1 (cut to pieces):

carve

WordNet sense 2 (separated into parts or laid open or penetrated with a sharp edge or instrument):

cut

WordNet sense 3 (separate into isolated compartments or categories):

compartmentalize, compartmentalise

WordNet sense 4 (destroy or injure severely):

mangle, mutilate

WordNet sense 5 (significantly cut up a manuscript):

hack