What is the best (in terms of security) way to destroy old (but still working) credit card?
Best way? I'd say, melt it into a ball. However, I generally just aggressively attack them with scissors and throw various parts in various trash containers.
Call the bank and cancel the card. It's the only way to prevent it from being used, since any merchant with whom you've previously used the card, or anyone who otherwise already has the card data (including simply a photograph of the card) could theoretically run it in a card-not-present transaction.
Once you cancel the card, the physical plastic card is relatively useless.
But if you want the most certain way to destroy a card, then the only way that is 100% effective and guaranteed to be absolutely irreversible is burning/melting it.
It depends on how far your want to go, but my choice is:
Scrape a sharp pair of scissors across the magnetic strip on the back (thanks to the Mythbusters, it seems that running a regular magnet across the strip does not destroy the data).
For the smart chip, make multiple cuts straight thorough the centre of the chip.
Lastly, drop the remains into a cross cut shredder.
Nail the card to a small piece of 2X4 scrap wood that you can throw away later with the magnetic side up. Use a piece of sand paper on a block to sand down the magnetic strip and the signature box on the back of the card. Then use a drill to drill holes in each number on the card and through the microchip embedded in the card. Most of these things you will see from the back side, that's why I suggest nailing it with the magnetic strip facing up. However, some cards also have numbers inked on the front so you may have to first use sand paper on those spots on the front of the card first. Once you've destroyed the magnetic strip, the microchip, the numbers that are impressed into the card and any inked on identification information, you can throw the wood away nobody can get the info off of it after you've done all that. But anyway, I think the question was already answered, I just thought I'd put my 2 cents in too.
Shredder AND cancel it with the bank!