How do I delete a discussion in a course?
You can delete a discussion or graded discussion at any time.
Note: When Multiple Grading Periods are enabled in a course, graded discussions are not currently validated against closed grading periods. Deleting a graded discussion may affect the total grade for students in your course.
In Course Navigation, click the Discussions link. There are two ways to delete a discussion topic.
Delete Discussion Topic from Discussions Index Page
To delete a discussion from the index page, locate the discussion. Click the Settings icon  and click the Delete link .