It depends. If the bills are in your name or they are joint between you and your spouse, then legally you have an obligation to pay them, whether or not you are living in the home or not. If your name is on the bills either solely or jointly, you absolutely must pay them. If you do not pay your mortgage, eventually the house will go into foreclosure. If you fail to pay your utilities, they will be shut off, and your credit score will likely be damaged.
If your name is not on the bills, and you move out, you may no longer be legally obligated to pay them, but you may have a moral obligation to pay them. If you have always paid the mortgage or the water bill, and you choose to move out during your divorce and quit paying them, if your spouse does not have the money to pay the bills, it’s probably a good idea to continue paying them. If you do not, your divorce is likely to get more difficult.
Instead of simply refusing to pay the bills, talk to your spouse about your finances now that you are getting a divorce. Ask him or her what type of financial contribution he or she can make towards the household, and what can be done to reduce your expenses. It may make sense for you to live with a family member of friend for free so that you can continue to honor your financial obligations.