How can I remove a coupon redeemed on a customer’s account?

Any coupon that's currently active on a customer's account can be removed both manually through the application's UI and with the developer API. You'll want to visit the customer's account details page and scroll down to the Coupons section. Once there, click on Manage Coupons and you'll be brought to a new page listing all active coupons on the account. Simply hover your mouse above the coupon you'd like to expire and click on Remove Coupon.

With the developer API you only need to utilize the following API call to remove any stored, active coupons on a customer's account page.