Exsanguination (or bleeding out) is the main cause of death when you are losing blood fast.
The average human adult I think, has approximately 8 pints of blood in their body at any given time, if not bleeding. This includes both blood that is oxygenated and not oxygenated. To lose 4 pints of blood would be a serious injury. Indeed, it would be VERY difficult to survive losing that amount, as that is basically losing around 85% of your total blood volume.
Here are some statistics to help. There are 4 stages of Hypovolemic Shock, which results from not blood, but specifically blood plasma, which is the liquid part of blood. By stage 3, you have lost probably around 35% of your blood volume. In this case, it is POSSIBLE that you may live with immediate transplant or treatment. beyond that is a stage 4 Hypovolemic Shock, which is around 45 to 50 percent of your blood volume gone. By this stage, you will be so far in shock that you may not even realize you are dying. This stage is extremely FATAL. Sadly, most patients die in this stage, due to organ failure as your body begins to shut down.
So, given that scale, if you lose around 45 to 50 percent of your blood, which is around....3.5 pints or so......you are most likely going to die.
So, to answer your question, losing 4 pints of blood is fatal, yes.