There are three good ways to kill dandelions naturally. The quickest, but hardest on your knees, is to dig them up, being sure to get the whole root. Other than that, you can spray them with vinegar on a hot sunny day. The vinegar will kill the leaves, but it may come up again from the root. When it comes up again spray it with vinegar again. It may take two or three times. Another good method is to pour boiling, or as hot as you can have it after you carry your tea kettle outside, water on it. Like the vinegar, you will probably have to do that two or three times before the root gives up.