A site user with Admin privileges can clear a customer account's payment method. From the customer account page, you will find the "Billing Info" box below their Account Info in the righthand column. Simply click "Edit" beside the Billing Info title, and a red "Clear Billing Information" button will be visible to admin users at the top of the page.
When using the API, you can clear billing info by using the "Clear Account's Billing Info" request, noted here.
You can also close out the customer account, which will remove their billing information and cancel any active subscriptions.