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.
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.
Keep in mind the average time for an ambulance to arrive is 12 to 15 minutes. Having a trained person and proper equipment such as an AED is critical. Unfortunately people wait until there has been an emergency before getting proper emergeny equipment.