Session are indeed faster and less of a headache, however, they don't allow a persistant shopping cart between visits.
If you do use a database table for your shopping cart, each entry should have some type of unique identifier. Then when the user deletes that entry from their shopping cart, you can simply delete from the table based on the unique identifier:
DELETE from shopping_cart_items WHERE cart_item_id='{$_POST['cart_item_id']}'
... or however you want to specify the id from the webpage.