Are any foreign divorces recognized by the state of Minnesota?

Yes, a divorce would generally be recognized as a matter of comity.  The key word is "generally."  There are exceptions.  The federal government generally has nothing to say about marriage law.  It is a matter left to each state.  With the sole exception of the federal law prohibiting the federal government or any state from recognizing a marriage or divorce of a same sex couple in a state or foreign country that allows it.  This strange law, called (DOMA, for Defense of Marriage Act), abridges the rights of the state governments in that one area. Otherwise, it is a matter of the individual state and its recognition of what occurred elsewhere.