While an expired or cancelled credit card should not work, banks still recommend that they are cut in half for security reasons. This practice comes from a time when all shopping was done in physical stores. 

It's also just a useful way to make sure you don't try use an old card.

Other plastic cards

Note that other types of plastic cards (eg hotel room key, plastic membership cards, points cards, etc) are not recyclable either and should be discarded in the trash.