I got married last year over seas. How do I go about getting a divorce? I never added my husband on taxes. So does the marriage count in the US if I was to get married here?

You are married in the US if you got married over seas. Not sure what "adding him on the taxes is" but married is still married.

Well I did not know that I can claim him on taxes since he does not ss yet, until I read other threads about ITIN or something.

But would divorce process be the same, should I claim in US or overseas?

You are married everywhere. You divorce him wherever you currently reside.