Loss of consciousness is the first sign
With blood loss, first you become unconscious due to the brain becoming starved of oxygen, then death follows as the brain cells fail. Think of cases where people fall thru the ice. Because of the cold, deterioration of the brain takes longer, so often those who've been "drowned" for minutes are capable of being revived, altho sometimes with brain damage.
The heart is a small target, but a large cut would work rapidly. Major arteries or the lungs take a little longer. My son bowshot a deer but missed the heart, shearing two ribs and severely piercing the lungs. The deer made about three hundred yards before collapsing, and who knows how much longer to die. As blood pressure drops the rate of flow slows.
Additionally, posture might be important, as someone lying down with legs elevated would be expected to retain conciousness slightly longer.