mouth off vs speak

mouth off and speak both are verbs.

Word	Noun	Adjective	Verb	Adverb
mouth off	No	No	Yes	No
speak	No	No	Yes	No

As verbs, speak is a hypernym of mouth off; that is, speak is a word with a broader meaning than mouth off:

Other hypernyms of mouth off include mouth, talk, utter, verbalise, verbalize.

mouth off (verb)	speak (verb)
talk in a noisy, excited, or declamatory manner	express in speech
	exchange thoughts; talk with
	use language
	give a speech to
	make a characteristic or natural sound