It depends on the cancellation policies that you set forth for your business. If you allow such cancellations, you simply confirm the customer's intent to cancel and update the status of the thier order to cancelled.
Follow these steps to cancel a customer's order while it is in the processing stage: Login to your account, click the “My Account” link in the top right, then select the “My Business Orders” tab. Choose the customer's order from the list; if you have too many orders in your list, you may limit the items displayed to only reflect orders that are in the processing stage by selecting “processing” from the order status dropdown in the search box and selecting “apply”. Once you're on the order details page, click the “Edit” tab, change the status of the order from processing to cancelled, add a note to the customer, then click the “Save” button.
After you mark the order as cancelled, the cancelled order status will be reflected on the customer's end. In addition, the customer will receive a email confirmation letting them know their order is cancelled along with any customer notes that were added.