Is mightn't noun or verb

The Word mightn't is a contraction, a shortened form of the auxiliary verb 'might' and the adverb 'not'.

'Might not' is most commonly used to express negative possibility:

Sandy might not have taken the bus.

Sandy mightn't have taken the bus.

A noun is a Word for a person, a place, or a thing.

The Words 'Sandy' and 'bus' are the nouns in the example sentence. The noun 'Sandy' is a Word for a person; the noun 'bus' is a Word for a thing.