In order to have standing to proceed with a marriage dissolution in Minnesota, the petitioning party must have resided (or been domiciled) in Minnesota for at least 180 days. When gay marriage was legalized in Minnesota, however, a new exception to that rule emerged. The reason for the exception is the fact that there are jurisdictions elsewhere that do not recognize same sex marriages.
If the marriage was performed in Minnesota, and both spouses reside where gay marriage is not recognized, either party can proceed with the divorce in Minnesota. The case is, of course, governed by Minnesota law, and not the law where the petitioning spouse resides.