Blood can come out of a human body at an amazing speed, and the first choice you have to make is whether or not there is any point at all even trying to control the situation. That may sound harsh, but your decision can make the difference between life and death for others involved in the event, or even your own future survival if you use everything you have trying to save someone who has no hope of survival.
In order for the heart to pump it has to have adequate pressure, and this is supplied by the veins and arteries of the body. It's a closed system. If that system is breached the blood pressure starts to drop which has an almost immediate effect on the heart. It's also possible that air enters via a severed vessel and that an embolism occurs, causing death.
So, the name of the game is to keep the blood pressure at a working level. Arterial blood is under much greater pressure than venous blood, so a person will bleed out from a severed artery much more quickly than they will from a severed vein. Job number one therefore is to decide if all the blood you are seeing is arterial or venous, because that makes a difference to what happens next.