Currently, this is the only known way to "cancel" a credit card attached to an XBOX Live account(or to any Microsoft service, apparently). After 36 minutes on the phone, not one of the three operators (Jian - Billing, Alfred - Billing Supervisor, RJ - Technical Support, all of them courteous) could remove my credit card information from my account.
Apparently, just like me, they have no way, no method to delete the information from the account. In other words, they have never programmed an interface to remove a credit card from an account. I can understand limiting access to credit card information as a form of data security to prevent it from being stolen or revealed to unwanted parties. However, deletion of the data is not possible. This is bizarre, especially considering that parents may not want their children to jack up the credit card that's attached to their account. Moreover, EVERY SCREEN in Xbox Live Marketplace says "(X) Add Microsoft Points" at the bottom - they make it easy to spend money.
Another thing that makes this whole thing awkward is that I only entered my credit card information in order to
get 1 year of Live Gold service. 1 year, that's it. Apparently, buying one year via credit card means that you are also set to auto-renew your account after that year is over, which is a transaction I NEVER authorized. I HATE auto-renewing stuff. Worse, there is no way to disable auto-renewal in Xbox Live account settings - you have to call Microsoft billing. I believe that this kind of behavior is best described by words like "dickish".
So, the only way to "cancel" my account is to log in to billing.microsoft.com and enter bad information to attach to the credit card number with a "valid" expiration date and a valid city and state(for the US at least). I say "valid" expiration date because the web interface doesn't allow for already expired dates, so I chose this month.