There are a number of issues regarding divorcing someone who currently lives outside of the country. The greatest issue here is related to "personal jurisdiction". Personal jurisdiction means that a court in a certain county, state, or country has the power to hear a case to which you are a party, and to enforce rules and judgments against you. If you were married within the United States and kept your marital home within the U.S., depending on the state you lived in with your spouse, you can file for divorce in such state. However, if you lived outside of the country with your spouse and have not lived in the United States with that person, you will be required to file for divorce in the country where you lived. Each state has different rules regarding when and how long you are required to have lived there for that state to have personal jurisdiction over you and your spouse.
Another major issue is going to be serving your spouse with the divorce documents while he or she is living in another country. Again, each country has its own rules and procedures, so I would advise that you contact an attorney who is familiar with service of process in your spouse's country.
