Blood vessels near the cut constricted is the mechanism that her body used to minimize the blood loss.
The mechanism in which blood vessels near the cut becomes constricted to prevent blood loss is known as vasoconstriction. This mechanism is the first response of the blood vessel to damage and it is initiated by vascular smooth muscle cells. Immediately a blood vessel is injured (cut), the blood vessel near the cut will constrict (narrow) which will make the blood flow through the affected area to be blocked or minimized. This way the amount of blood loss is reduced.