The circulatory system is a vast network of organs and vessels that is responsible for the flow of blood, nutrients, oxygen and other gases, and hormones to and from cells. Without the circulatory system, the body would not be able to fight disease or maintain a stable internal environment - such as proper temperature and pH - known as homeostasis.
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Imagine if you die. You begin to rot. No oxygen flowing to your leg would result in cells dying off and rotting away, with that said new cells can't be formed. Eventually if the leg is still attached to you then your leg would be unable to fight infection, which would spread until you actually die. That is why they amputate legs that no longer have blood flow.
without your circulatory system your body would completely shutdown because your body would not get the nutrients needed to survive.