Since Luxe is an upgrade to the Base subscription, you can cancel your Luxe upgrade without canceling your BoxyCharm subscription.
To cancel your Luxe upgrade, log in to your account at www.boxycharm.com and click My Account from the top menu bar, then click Subscriptions from the dropdown menu. Find your Luxe subscription and click Cancel, then follow the steps until the cancellation is confirmed. Your Base subscription will remain Active.