The only way that paying off the mortgage on your home could increase your tax is if you itemize deductions on your tax return. After paying off the mortgage you would no longer have a deduction for mortgage interest, so your tax might increase. (But you also are no longer paying the interest. The cost of paying the interest is much higher than the amount of tax that you save from the deduction, so it's a net saving overall, even if you pay more tax.)
The amount that your tax would increase depends the amount of mortgage interest, your other itemized deductions, your tax bracket, and other factors. The easiest way to calculate the difference would be to prepare what-if tax returns with and without the mortgage interest deduction and see how much difference it makes.
As DoninGA said, if you do not itemize deductions, paying off your mortgage will not make any difference in your tax.
