It depends on the source of the hemorrhage. Exsanguination is the term for bleeding to death. If the bleeding is from an arterial source, death may only take 20 seconds to a couple of minutes. Keep in mind though that the particular artery involved will determine how quickly you bleed out. If the blood vessel is a large one like the abdominal aorta, and if this vessel was lacerated in half, then massive hemorrhage ensues and death comes in literally 20-25 seconds. If the artery is smaller in size, and no first aid was received by the victim, then death will come in 2-3 minutes.
Acute bleeding from a venous source takes a longer period of time to cause damage and death. Here again, it depends on the location of and size of the vein. Damage to larger veins like the superior vena cava will result in death in 4-6 minutes. Bleeding from smaller veins will take longer, assuming of course, that no first aid was received.