Only contests in the Drafts section can be deleted off of your account (Any unscheduled promotion is a draft). If you have already scheduled a promotion, but still want to delete it, just delete out the start and end dates and times. This will move the promotion back to drafts where it can be deleted.
Completed contests will be automatically be moved to the Completed Promotions section after 2 weeks. However, you can change this timeframe by clicking "More Grid Settings" button under the Active Grid title.