Let me add my 2 cents here for thought - Do your customers pay at the time of the order? If so the charge is already processed.
You have the ability to initiate a refund action from within your cart processors dashboard, but not directly from within your cart. This is a good thing - so that management is approving and authorizing refunds.
You can change the status of the order to whatever designation you wish - cancelled, refunded, etc. This is a manual process.
You can also issue a credit to your customer if you wish, and that can be applied to their invoice. You could use this for also adding to their account and sending the a new invoice for the difference. You can read about that here:
http://docs.abantecart.com/pages/customers/transactions.htmlJust think about what happens when you pay for something in person in a store with a card or a check - once it is rung up the transaction is completed. If you return an item, they give you a refund - a separate transaction. If you pick up another item after the first transaction - you get out your credit card or your check book and pay for that transaction. Online works the same way.
Hope this helps you.
Lee