1) Go to cart page and click on [Edit] link. You will be now in product page.
2) Change quantity to zero and click on [Update] button
This should remove the product from cart. You will get again cart page with quantity unchanged.
3) Now change in cart page quantity to zero and update it. The product will be remove from cart which is a correct behavior.
Maintenance team - Please change the script to allow zero quantities in product page then delete the product from cart. Thank you