What method would you use to separate sand and water?

A mixture of clay and water is a physical and not a chemical mixture. Physical means will separate them, and the easiest way to do that is probably just to filter the mixture. The water will pass through an appropriate filter, and the clay will remain. Use three or four coffee filters together and pretty much only some dissolved materials will come through with the water. This will leave the clay behind. Spread out the clay, and it will finish drying by itself.