Bunch of related, but different, concepts floating around here.
1. To purge Holy City status, conquer the city and zap it with an inquisitor of your religion. Unless the religion has taken the Unity of the Prophets Reformation belief, Holy City status is extinguished, so no more internal Holy City pressure, even if the zapped religion re-spreads to the former holy city.
2. Inquisitor zapping also removes current followers of that religion from the former Holy City (which a Great Prophet also could do), but it does not eliminate that religion from other cities or preclude that religion from re-spreading to the former holy city. Religiion could re-spread either through passive pressure (if there are enough neighboring cities that are still majority that religon to out-pressure your religion) or through manual spread (the AI can send missionaries and Great Prophets to try to reconvert the city).
3. The only way to truly elimiinate a religion from the map is to (1) completely eliminate the founder of that religion (so no more GPs of that religion can spawn) AND (2) make that religion a minority in every city where it appears (so the religion exerts no pressure on other cities) AND (3) find and kill every wandering GP, missionary and inquisitor of that religion (for obvious reasons). Until the founder is dead and gone, he or she can still spawn a Great Prophet of his or her religion and start the re-spread. Similarly, if any civ still has a city with a majority of that religion it can spawn a misisonary and keep spreading the religion. (I've seen this in far too many games--kill the founder and some other nitwit AI keeps spreading the dead founder's religion.)