In medicine, something that's styptic is meant to stop the flow of blood. Some people have styptic pencils in their medicine cabinets in case they cut themselves shaving.
Styptic agents (like styptic pencils) slow bleeding from cuts. They contain astringents that work to contract tissue and seal blood vessels, and before the invention of safety razors, they were a common part of shaving kits. The Greek root of styptic is styphein, "to constrict."