Once you've watched several minutes of a class, you'll automatically receive updates each time the teacher posts a new Discussion. If you don't want to receive notifications for a specific class, head to Email Notifications within your Account Settings. Under Updates from Classes You're Taking, click the "Edit Individual Classes" link , and uncheck that specific class.
Meanwhile, if you'd like to remove a class from the Your Classes section of your account, go to Continue Watching, select the Hide Classes I've Marked as Complete button, and then hover and choose Mark as Complete on any classes you'd like to remove from view.