push back vs beat back

push back is a noun but beat back is not a noun.

Word	Noun	Adjective	Verb	Adverb
push back	Yes	No	Yes	No
beat back	No	No	Yes	No

As verbs, push back and beat back are synonyms defined as:

Other synonyms of push back include drive, force back, repel, repulse.

push back (noun)	beat back (noun)
the act of forcing the enemy to withdraw

push back (verb)	beat back (verb)
cause to move back by force or influence	cause to move back by force or influence