Once you´ve paid off your mortgage, in order to get the debt lifted from the property records, you need to go through some administrative procedures.
You need to take the mortgage escritura plus a certificate from the bank that confirms the mortgage has been paid off to a notary. He will prepare the necessary paperwork that all parties have to sign. The bank will need to bring the original title deeds that they have had in their posession while the property was mortgaged. With the signed copy you go to the Registro de Propiedad in your area so they can process the document there. In a couple of days you can pick up a ´copia simple´ that will state that the property is free of debt.
You will have to pay for this procedure yourself, or the bank will do it for you, for a fee.