The easiest way to do this is to just not display the shoppingcart anywhere.
If you choose to do this, you might also want to delete any orderpage you might have (as there’s nothing to order).

Alternatively, if you still want to show the cart (to show combined prices/taxes/discounts) but want to disable ordering, you could copy wppizza-custom.css to your them directory and add “.wppizza-cart-button{display:none}” without the quotes to it. You can probably also achieve the same thing by using a combination of the layout and/or order setting options available from within the plugin.

You might still want to delete/hide your order page or at least disable all your gateways