1) To Delete a performance first, you need to Edit the event. Go to the "Box-Office Page", and select the performance you wish to delete. Click on "Edit" button to edit the event.
2) In the 'Event Info' menu go to the "Performance" tab and select the checkbox placed next to the performance you wish to Delete. Now click on the Delete button above.
(Note: Once a ticket is sold for a particular performance you cannot delete that performance)