Deleting or removing a product completely from the JVZoo system is impossible because of the complexity of click tracking, button tracking, sales tracking and for historical purposes. You can archive products and archiving them is virtually removing the product from everything and affiliates are unable to locate the product or put in a request to promote it in the future.
To archive the desired product simply locate the product you want to work on, select "edit product" and there is an option right above the save button "archive product". This removes the product and makes it inaccessible to everyone.
If you've made a mistake or you've changed your mind and you would like to reactivate your product to make further sales you can always un-archive it with the same instructions as above but instead of "archive product", you will need to choose "un-archive product".