cut-up vs bad hat

cut-up and bad hat both are nouns.

Word	Noun	Adjective	Verb	Adverb
cut-up	Yes	No	No	No
bad hat	Yes	No	No	No

As nouns, bad hat is a hypernym of cut-up; that is, bad hat is a word with a broader meaning than cut-up:

Other hypernyms of cut-up include mischief-maker, trouble maker, troublemaker, troubler.

cut-up (noun)	bad hat (noun)
someone who plays practical jokes on others	someone who deliberately stirs up trouble