From what I have read here, I understand that if I buy a tax deed in Florida and the owner never pays up, I will own the property free and clear? What about the mortgage the owner owed on the property? Will the mortgage holder not pay the taxes and get the property themselves? I don't understand how a mortgage can just "disappear" on a tax deed sale. Please explain.

Normally the mortgage lender will pay the taxes to protect their interest in the property. Do you have a specific property in mind or are just asking a general question?