Once you initiate your divorce, your partner will move out the next day and return to their original house. It is important to know that although most of Stardew is pleasant and wholesome, divorcing someone does change your relationship with them. They will become much more negative with you, and your relationship with them will reset back to zero hearts. It will be harder to engage with them moving forward, and they will be regarded as your ''Ex'' on the characters tab within the in-game menu.