Clean Cart On Payment Processor Response

Is any possibility to clear customer cart, after payment processor change status to "Paid"? Unfortunately, the customer is not redirected back from payment to shop, so we can't clear cart from the session. And we can't clear cart before we redirect a customer from shop to payment processor page.
So, if the customer e.g. has opened shop in two windows, still have products in the cart, and can pay once again for the same order.