take away vs cross out

take away and cross out both are verbs.

Word	Noun	Adjective	Verb	Adverb
take away	No	No	Yes	No
cross out	No	No	Yes	No

As verbs, cross out is a hyponym of take away; that is, cross out is a word with a more specific, narrower meaning than take away:

take away (verb)	cross out (verb)
take out or remove	remove from a list
remove something concrete, as by lifting, pushing, or taking off, or remove something abstract
get rid of something abstract
take away a part from; diminish
buy and consume food from a restaurant or establishment that sells prepared food
remove from a certain place, environment, or mental or emotional state; transport into a new location or state
take from a person or place