You cannot delete an auction.

Option 1: Re-Use the Auction

You can however remove any items and then re-purpose the auction by editing the name and settings, etc.

Option 2: Archive the Auction

Go to the Auction List view and Archive the auction by hitting the Archive button in the actions column of the Auction.

You can also Hide the auction by ticking Hide in the Auction List view, which will make sure the auction doesn't show in your Past Auctions list.