CartModifierFormHandler has a String array removalCommerceIds which you need to set with the ids of commerce items that you want to remove, in your case, with ids of all the items in your order.
Then call handleRemoveItemFromOrder method which in turn calls deleteItems method to remove the commerce items from the order.
Please refer the below link for more details about these methods.
Hope this helps.
Keep posting the updates / questions.
( This is one functionality that no ecommerce site is willing to provide :-))