No. Currently there is no way to permanently delete a Ving from your account. However, you are able to archive old Vings from your homepage.
You can archive a Ving by marking it inactive. This will prevent anyone from having access to an old Ving you no longer want anyone to view.
Click here to learn How To: Archive a Ving.
Vings that have been archived will appear in your archived folder, along with any old inactive revisions.