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.
Delete Discussion Topic from Discussions Index Page
Click the Settings icon next to the discussion you want to delete. Click the Delete link.
Click the title of the discussion.