How long can you live with a severed artery?

It depends on which artery. If your femoral artery is severed, you have minutes to live without immediate medical attention. Same for the Carotid artery in your neck, or the jugular vein in your neck. If the aorta artery feeding your heart goes, same thing. I would say the smaller the artery, the longer you may have to live before you bleed out.

The biggest life threat as far as arterial bleeds is the aorta. If any part of the aorta ruptures, a surgeon couldn't save you if he already had you cut open on the table. Essentially, if the aorta ruptures, it will only take about 3 beats of the heart to bleed out. The further away from the heart you get, the slower the bleed will be, but any compromised artery is potentially life threatening. The femoral artery in the thigh (the femur is the thigh bone, hence the name fermoral) is another big bleeder. The carotid is the second biggest life threat if it's compromised. So basically, if the aorta ruptures, 3 heart beats. If the carotid ruptures, perhaps 2 minutes. If the femoral is severed, perhaps 5 minutes. The difference is that the carotid and the femoral arteries can be controlled with proper treatment. The aorta is untreatable once it's compromised.