A spouse living abroad does not prevent a New York divorce, provided New York is the right place to file. The complications are about jurisdiction and how the papers get delivered.
Can New York hear it
New York has residency requirements that have to be met before a court will take the case. They turn on how long you have lived here and where the marriage and its events are connected.
This is the first thing to check, because everything else follows from it.
Getting papers to another country
Service abroad follows international rules rather than the ordinary New York method. Many countries are party to the Hague Service Convention, which sets out a formal channel through a designated authority.
Countries outside that convention have their own routes. Either way it takes longer than domestic service and it needs to be done correctly, because bad service can undo a judgment later.
Where it gets easier
If your spouse is willing to cooperate, they can sign an affidavit accepting service, and much of the international complication falls away.
This page is general information about how the process works in New York. It is not legal advice and it does not create an attorney-client relationship. Whether any of it applies to you depends on your situation, which is what a consultation is for.