Will one ex-spouse’s Offer in Compromise absolve the other ex-spouse from liability?

First, the IRS does not care what your state court divorce order says.  Since you and your ex-wife filed jointly, you both are jointly and severally liable for the entire tax bill.  This means that you both owe the entire amount and the IRS can pursue either or both of you for payment.  However, once the entire amount is paid neither will owe anything, i.e. they only collect the total tax once and will not collect the entire amount from both of you. Therefore, the IRS can pursue your ex-wife to collect the amount of taxes still due after your Offer is paid.  If they do, your ex-wife can then file a Rule To Show Cause against you in Family Court to have you held in contempt for failing to obey the Court’s Order. This can result in fines and/or jail time.