AMT is essentially a separate tax system, one that does not care one bit about how much you pay for your mortgage. You end up paying the higher of what the AMT system says you owe compared to what the non-AMT system says you owe. If you're paying AMT, getting rid of your mortgage interest won't cause your taxes to go down. If anything, it could cause your taxes to go up if it would cause your tax under the non-AMT system to be higher than your tax under the AMT system.