How do I put an 'if clause' in an SQL string?

Since MySQL doesn't support if exists(*Your condition*) (*Write your query*), you can achieve an 'if clause' by writing like this:

(*Write your insert or update query*) where not exists (*Your condition*)

For your specific query, you can do:

UPDATE purchaseOrder
    SET purchaseOrder_status = 'COMPLETED'
    WHERE purchaseOrder_ID = '@purchaseOrder_ID' and
          not exists (SELECT *
                      FROM itemsOrdered WHERE purchaseOrder_ID = '@purchaseOrdered_ID' AND status = 'PENDING'
                     )

However, I might guess that you are looping at a higher level. To set all such values, try this:

UPDATE purchaseOrder
    SET purchaseOrder_status = 'COMPLETED'
    WHERE not exists (SELECT 1
                      FROM itemsOrdered
                      WHERE itemsOrdered.purchaseOrder_ID = purchaseOrder.purchaseOrdered_ID AND
                            status = 'PENDING'
                      limit 1
                     )

You can use the multiple-table UPDATE syntax to effect an ANTI-JOIN between purchaseOrder and itemsOrdered:

UPDATE purchaseOrder p LEFT JOIN itemsOrdered i
    ON p.purchaseOrder_ID = i.purchaseOrder_ID
   AND i.status = 'PENDING'
SET    p.purchaseOrder_status = 'COMPLETED'
WHERE  p.purchaseOrder_ID = '@purchaseOrder_ID'
   AND i.purchaseOrder_ID IS NULL