Hi Mandy,
Ariba won't allow to delete a PO but you could cancel an order which will create a second version of the PO and will send out a PO cancellation request to the vendor. Cancel button will be available on top of the requisition if it is ordered status. A fully or partially received order cannot be cancelled but if there are any received items in a PO, then you could submit negative receipt to nullify the total received items back to 0, and then cancel button will be visible on the requisition.
Thanks & Regards,
Amit