The Jet.com API works in update mode, not in “purge and replace”, which means if no information is sent concerning a product it will just stay the same.
You need to delete your products on Jet.com directly in order to remove it. An other way is to mark the product as “Disabled” in your product sheet and send an update to Jet.com, it will delete the product. Once the product is deleted on Jet.com you can delete it from your shop.