Nothing stings like a nick from a razor, and once the blood starts to flow, it is even worse. Luckily, there are few things you can do to stop the bleeding, such as using a styptic pencil or rubbing a dab of antiperspirant or lip balm on the cut. The aluminum chloride in the antiperspirant helps to slow the blood flow and stop the bleeding; while the wax in the lip balm helps seal off the cut and stop the bleeding.
If you dont have either of those items handy, you can use a washcloth soaked in hot water. You will need to hold the washcloth firmly to the cut to help the bleeding subside. Sugar is also a great alternative to use, as it will not only stop the bleeding, but also acts as a disinfectant. If sugar is not handy, you can make a paste out of aspirin and water, which will also help to soothe any irritation caused by the cut.