I was hoping someone with more medical knowledge might answer this. I'm a former EMT/firefighter, so I'd be more informed about the field treatment than the what happens in the hospital.
It is possible that a stab wound could cause a significant loss of blood. It would not be likely, but if someone hacked the arm almost all the way off ...
Okay, here comes the brief lesson on blood loss --
The average adult has between 10 - 12 pints of blood (weight of 150 pounds). A pint of blood is usually referred to as a 'unit.' There are four classes of blood loss. Class 1 is up to 15% (1.5 units) and has little or no effect. To see how much blood loss is involved, take your measuring cup, take some red food color, and spill three cups of water on the kitchen floor. Big mess and if you walked in on a scene like this, you'd be in a state of shock.
Class 2 is up to 30% (3 units) blood loss. Add three more cups onto the floor. You're beginning to see signs, patient would be pale, blood pressure narrows, pulse increases, breathing increases. Skin would be cool, pale and dry.
Class 3 is up to 40% (4 units) blood loss. Add two more cups onto the floor. Rapid heart rate, rapid respiration, cool, clammy extremities. Patient would be confused, restless, and anxious. Medical emergency. Lights and siren all the way to the hospital. One, probably two large bore IV's running. Supplemental oxygen. Call to ED to let them know what they're getting. Surgical team would be notified. I'm guessing there would probably be a transfusion at the hospital. By the way, your floor is a mess. Until you've walked into a scene with this amount of blood loss, you won't believe how much blood is in a human being.
Class 4 is more than 40% (4 units) of blood loss. Patient is rapidly bleeding out. Hopefully patient has a will, because more likely than not, they're going to need it. Incredible amount of blood is the person is not bleeding into themselves. Everything will be red. Patient is only marginally responsive. Blood pressure probably unreadable. This is what is called professionally, an "oh, shit" call. Like when you walk in on the scene and go, "Oh, shit."
Tests are: blood pressure, capillary refill, pulse, respiration, observation (when EMT tells the doctor "Oh my God, there was blood everywhere.").
On the hospital end, the test would be for blood type. Here's where I don't know too much. I believe that in cases involving large amount of blood losses, they put blood in before matching is done, but I'm not sure. Class 3 and 4 go through the ED and up to the operating room before the ambulance leaves the hospital (cleaning takes a while in these cases).
Other than suicide, it's hard to get the blood loss with an arm injury. You really have to know what you're doing. I'd add a couple wounds to the stomach to get up to a Class 3 blood loss. The other alternative is a lot of hacking damage to the arm, but chances of full recovery to the arm would be unlikely. Good possibility of amputation.
I hope this helps.
Jim Clark-Dawe
After reviewing this, I remembered that a unit is 1 liter of blood, not one pint. I don't remember the conversion between the two.