put away vs eat up

put away and eat up both are verbs.

Word	Noun	Adjective	Verb	Adverb
put away	No	No	Yes	No
eat up	No	No	Yes	No

As verbs, eat up is a hypernym of put away; that is, eat up is a word with a broader meaning than put away:

Other hypernyms of put away include finish, polish off.

put away (verb)	eat up (verb)
turn away from and put aside, perhaps temporarily	finish eating all the food on one's plate or on the table
eat up; usually refers to a considerable quantity of food	use up (resources or materials)
kill gently, as with an injection	enclose or envelop completely, as if by swallowing
place in a place where something cannot be removed or someone cannot escape
stop using
throw or cast away
lock up or confine, in or as in a jail