Whether someone can get divorced in the United States is actually both a fairly simple and a very complex question.
First for the simple part. Essentially, if one of the spouses is “domiciled” anywhere in the United States, then the court in their place of domicile can divorce them.
Now it gets complicated pretty fast. “Domicile” in this context does not mean just where someone lives. Domicile in the legal context means where the persons is physically present with the intent to remain indefinitely. You can only ever have one domicile at a time, and you cannot have no domicile. Your domicile of origin stays your domicile until you have clearly abandoned it for a new domicile.
So you can see how the question of domicile can be complicated and very fact-dependent. It depends on lots of things in addition to just where you are living at the time. Citizenship and the legal ability to stay in a place indefinitely is one element. Whether an absence is intended to be more or less permanent, or only temporary, also is important. Facts such as where a person owns property, works and pays taxes, votes, receives mail, banks, has a driver’s license, and family ties, all can come into play.
And even then, domicile does not answer the whole question. That is because the court of a person’s domicile, under the U.S. approach, can decide divorce, but may be unable to divide marital property, award alimony or child support, or decide custody. All those decisions depend on factors different from domicile.
So the key in any divorce situation, especially where more than one court system might be involved, is to get a knowledgeable lawyer to review all the facts, weigh the options, and advise on what may or may not be possible—as early as you possibly can.