ionized water treats cancer in three major ways. Because it is a good antioxidant, alkaline ionized water has a very negative ORP value (Oxidation Reduction Potential), it neutralizes free radicals (i.e. ROS - Reactive Oxygen Species), making many oxygen molecules available to the cancer cells; either to slow the growth of cancer or to kill the cancer cells. This is done with the hydroxyl ions in the alkaline ionized water.
Unlike hydrogen peroxide, which adds oxygen molecules to the body (i.e. they don't already exist in the body), alkaline ionized water makes existing oxygen molecules, already in the body, available to the cancer cells by giving them electrons. This actually has advantages because it removes damaging free radicals at the same time.