Is except an adverb or adjective?

It isn't either. Except is a preposition or less frequently a conjunction or verb.

Preposition:

"They called everyone except me."

"It was a great day except for the wind." (idiomatic form)

Conjunction:

"I'd love to come except I don't have any money." (but)

Verb:

"The city was excepted from eligibility." (excluded)