With interest rates so low, keep the car (I assume it is paid for). Make an extra mortgage payment or two each year. better off having the interest deduction.
Why do people continue to think that having a mortgage is a good thing because you can deduct the interest on your federal tax return? Simple math will show you that the cash outflows far exceed the benefit you get from the reduction in taxes. If the reverse were true, we should all go out and finance multiple properties because we would be generating income from all the interest we were paying. And we would look to refinance as soon as the rates went up, not down. LOL There are good reasons to have a mortgage, but being able to deduct interest isn't one of them.
It boils down to what you need more, the car or the money. Since you're thinking of selling, you must need the monthly cash flow. If you sell the car and pay the house off, you can always get back into another S2000 or something different down the road if things get better, financially. If it's not a monetary strain to keep the car and make payments on the house, then do it. You must be close to having it paid off, anyway, if the sale of the car would be enough to pay off the mortgage.
Good luck with your decision.