Is it possible to add or remove a "Sale" on the images?

I want to add or remove the "Sale" label for products that are on sale or have discount promos displaying on the upsell section. Is this possible?

Absolutely! You can show or hide the Sale tagging or badge on an upsell item at any given time. This setting is just a press of a button. Check out this article on how to show sale badge on images for more info.