Your divorce decree is a contract between you and your ex-spouse. This is completely separate from any contractual obligations you have with your mortgage lender or your credit card company.
Therefore, if you have a joint debt, even though your divorce decree says your ex-spouse will assume all the debt, your creditors can still come after you for the debt. For example, suppose you and your ex-spouse had a joint credit card with Bank of America for $20,000. During your divorce, your spouse assumes payment of the $20,000 debt. Your ex-spouse does not make a payment on this debt or files for bankruptcy. Bank of America can come after you for the $20,000 debt. If this happens you would need to pay it or file for bankruptcy. If you end up having to pay a anything to Bank of America you would have a cause of action against your ex-spouse once you have re-paid the creditor. If you and your spouse have significant amount of joint debt, it maybe beneficial to consider bankruptcy prior to filing for divorce to resolve these issues that may cost you more down the road in payments to creditors and additional attorney fees.