Yes, only one spouse needs to reside in Minnesota in order to get a Divorce. Importantly, you must be living in Minnesota for at least 180 days (approximately 6 months) before you can bring an action for Divorce in Minnesota.
A spouse starts the Divorce process by “serving” a Summons and Petition on the other spouse. There are specific rules about service, including that the document must be personally served (handed to the person being served). However, you can also prepare an Affidavit of Service that the other party can sign (in front of a notary), acknowledging they have received the Summons and Petition, and return the signed document to you/your attorney.
Service can still be accomplished if your spouse resides in a different state. If you are unsure where your spouse is living, have no way to contact them, or think they will avoid service, these issues can also be overcome by discussing your options with an attorney.