Those are old movies.
If a credit card had been cut in half, no merchant is required to accept such a credit card, no matter what excuse the customer (card holder) gives.
Many years ago there was no credit card readers, so all credit card transactions involved imprinting the raised numbers of the card onto a special paper invoice and the customer signed that invoice, and got one copy of it and the merchant kept the other copy.
Once a week the merchant would get a small booklet from the credit card companies - Visa and Mastercard - which listed all the cards that were NOT to be accepted. When a new booklet came in, the older booklets were to be trashed as being out of date.
The rules were that if a customer presented a card that matched the number in the booklet, the merchant was to NOT return the card to the customer and send that card to the bank processing the credit cards for the merchant. If a customer objected to the merchant taking the credit card from them (after all, a customer has a right to worry that a merchant's employee might intend to put fraudulent charges on that card) then the merchant was to cut the card in half, which was to satisfy the customer's concern.
Some of the numbers in the booklet were of cards where the customer had be delinquent in paying their bills. Some of the numbers in the booklet were of stolen cards.
So the TV and movies are right - each merchant had their own little ritual they used to destroy a declined card. But these days, with electronic verification, no merchant is going to bother cutting a credit card with a pair of scissors. Besides, if the card is a stolen card or a counterfeit card, that would be destroying evidence, and prosecutors would very much like it that evidence is not compromised.
