strong-arm vs beat up

strong-arm is an adjective but beat up is not an adjective.

Word	Noun	Adjective	Verb	Adverb
strong-arm	No	Yes	Yes	No
beat up	No	No	Yes	No

As verbs, beat up is a hypernym of strong-arm; that is, beat up is a word with a broader meaning than strong-arm:

strong-arm: use physical force against
beat up: give a beating to; subject to a beating, either as a punishment or as an act of aggression

Other hypernyms of strong-arm include beat, work over.

strong-arm (adjective)	beat up (adjective)
impelled by physical force especially against resistance

strong-arm (verb)	beat up (verb)
use physical force against	gather
be bossy towards	give a beating to; subject to a beating, either as a punishment or as an act of aggression
use force against