break off vs cut off

break off is not an adjective while cut off is an adjective.

Word	Noun	Adjective	Verb	Adverb
break off	No	No	Yes	No
cut off	No	Yes	Yes	No

As verbs, cut off is a hyponym of break off; that is, cut off is a word with a more specific, narrower meaning than break off:

Other hyponyms of break off include fracture, bog, bog down, break up, disrupt, interrupt.

As verbs, break off and cut off are synonyms defined as:

Other synonyms of break off include chip, knap.

break off (adjective)	cut off (adjective)
	detached by cutting

break off (verb)	cut off (verb)
prevent completion	cease, stop
interrupt before its natural or planned end	make a break in
break a small piece off from	remove by or as if by cutting
break off (a piece from a whole)	remove surgically
break a piece from a whole	break a small piece off from
	cut off and stop