If a piece of property is purchased at a property tax sale and has a morgage what happens to the morgage?

If what you purchased isn't actually the property, but a tax sale certificate, you don't own the land, just the right to be paid back the taxes you "bought" plus interest that's usually at a very hefty rate, when the land is sold either by the owner or through a foreclosure.

If the tax sale certificate was itself foreclosed (and, after you've held the tax sale certificate for a certain period of time, you can have it foreclosed yourself) and the property sold at auction, the sheriff's sale buyer takes the property free of the mortgage.  The mortgage gets paid out of the proceeds of sale, after the taxes, and if there's any unpaid balance left over, the mortgage company gets a deficiency judgment against its borrower.