mutual opposition vs opposition

mutual opposition and opposition both are nouns.

Word	Noun	Adjective	Verb	Adverb
mutual opposition	Yes	No	No	No
opposition	Yes	No	No	No

As nouns, opposition is a hypernym of mutual opposition; that is, opposition is a word with a broader meaning than mutual opposition:

Other hypernyms of mutual opposition include oppositeness.

mutual opposition (noun)	opposition (noun)
a relation between two opposite attributes or tendencies	the act of hostile groups opposing each other
	the action of opposing something that you disapprove or disagree with
	a body of people united in opposing something
	an armed adversary (especially a member of an opposing military force)
	a contestant that you are matched against
	a direction opposite to another
	the relation between opposed entities