paragraph vs carve up

paragraph is a noun but carve up is not a noun.

Word	Noun	Adjective	Verb	Adverb
paragraph	Yes	No	Yes	No
carve up	No	No	Yes	No

As verbs, carve up is a hypernym of paragraph; that is, carve up is a word with a broader meaning than paragraph:

Other hypernyms of paragraph include dissever, divide, separate, split, split up.

paragraph (noun)	carve up (noun)
one of several distinct subdivisions of a text intended to separate ideas; the beginning is usually marked by a new indented line

paragraph (verb)	carve up (verb)
write paragraphs; work as a paragrapher	separate into parts or portions
write about in a paragraph
divide into paragraphs, as of text