How do I cancel an Apple Cash account?

Howdy! Here are some instructions taken from the Apple Support website.

Before you close your account, make sure that your balance is $0 and that you don't have any pending transactions. After that, you'll need to contact Apple Support. You can do this by opening the Wallet app, then tap your Apple Cash card, then tap the "More" button (three dots), then tap "Card Details". From there tap "Contact Apple Support" and then "Call". You'll then be able to handle it with Apple Support over the phone.

For the full unparaphrased support document, see here:

Close your Apple Cash account or turn it off on a device - Apple Support

Hope this helps!