laugh away vs dismiss

laugh away and dismiss both are verbs.

Word	Noun	Adjective	Verb	Adverb
laugh away	No	No	Yes	No
dismiss	No	No	Yes	No

As verbs, dismiss is a hypernym of laugh away; that is, dismiss is a word with a broader meaning than laugh away:

laugh away: deal with a problem by laughing or pretending to be amused by it
dismiss: bar from attention or consideration

Other hypernyms of laugh away include brush aside, brush off, discount, disregard, ignore, push aside.

laugh away (verb)	dismiss (verb)
deal with a problem by laughing or pretending to be amused by it	declare void
	bar from attention or consideration
	end one's encounter with somebody by causing or permitting the person to leave
	cease to consider; put out of judicial consideration
	terminate the employment of; discharge from an office or position
	stop associating with