Hi, Horamakhet,
That is one very attractive cover.

In answer to your question, when a Pope dies, or in the case of Benedict XVI when he resigned, his ring is cut to symbolically indicate the end of his pontificate...but that is all that is associated with the Pope that is "destroyed" in any way.
The Philatelic and Numismatic Office of the Governorate of Vatican City State ("Ufficio Filatelico e Numismatico" or UFN) continues to sell previously printed stamps until the stock runs out, just like any postal service.
Even the much-sought Sede Vacante stamps, which are issued only in limited quantities during the period between the end of one pontificate and the election of a new Pope, are still sold by the UFN until the stock runs out--and are not withdrawn from sale when the new Pope takes office, as some may think.
Your cover was either CTO from the Vatican UFN as a souvenir, or someone affixed previously issued stamps to a postcard and had it cancelled on request, but either way the stamps were still valid for cancellation in 1997 even though Paul VI passed away in 1978.
--Kevin