In some potential cases, this might save you a bit of money over doing nothing. But, there are many better ways of doing it.
1) Like others have said, this is a risk. You would risk losing your home over a missed payment for your car. Your willingness to take that risk is not a good sign (neither was your choice to lease a car that you want to buy, but that is a story for another thread). The huge risk isn't balanced by a similarly large gain. At most you'll save a couple hundred dollars over doing nothing. So, are you willing to lose your house over a few hours worth of pay?
2) You haven't discussed even better options. For example, Thepd7's suggestion of just outright buying the car with cash. You should be able to do that if you can save almost $500/month. Of course, not everyone can afford to save at that rate. But, if you can't you probably couldn't truely afford that car either when you bought it.
3) The best option of all, is probably to just refinance your home at ~3% and take some of your equity out for the car. No second mortgage needed at all and you get that great rate on all of the mortgage balance instead of just $10k.
We cannot answer your question regarding tax savings since we don't know your tax rate nor do we know your deductions. Remember, only a part of mortgage interest is deductable (the part that is above the standard deduction). As interest rates go lower, and as time passes and your mortgage gets smaller, that tax deductable part gets smaller and smaller.