I am plainning to refinance my home and my mortgage company offered a "short payoff" in which I will receive a 1099 at the end of the year. Will I be required to pay taxes on this money?

Yes - any income shown on a 1099 must be reported to the IRS. If your bank is forgiving some of your debt, they are in effect making a gift to you, and this must be reported as income.

Yes you will have to pay taxes on this forgiven debt because any income that is
Claimed on a 1099 taxes have to be paid on it