take out vs cross off

take out and cross off both are verbs.

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

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

take out (verb)	cross off (verb)
take out or remove	remove from a list
prevent from being included or considered or accepted
take out of a literary work in order to cite or copy
buy and consume food from a restaurant or establishment that sells prepared food
remove something from a container or an enclosed space
remove from its packing
remove, usually with some force or effort; also used in an abstract sense
take liquid out of a container or well
bring, take, or pull out of a container or from under a cover
remove (a commodity) from (a supply source)
purchase prepared food to be eaten at home
obtain by legal or official process
make a date
cause to leave