I don't think cutting it up is a good idea. You can always try breaking the pill in half, or asking your doc for another method. I know they offer it in a liquid form, or you can get a lot of iron from a certain diet.
Iron will make you constipated, so I also suggest taking a good stool softner to help stay regular. You can find stool softners in powder form that are tasteless and oderless. I would try benefiber or miralax, both which are safe