Spend a lot of money and get yourself a packet of QuickClot. Pour some on the wound and it will clot instantly. Granted, it might burn a little, but you'll be fine. Then the fun part is rinsing all that **** out.
Purchase a Hemcon (i think its called) bandage, cut a small piece off, and put it right up to the blood vessel. Those are even more expensive though.
Tournequette around the neck will solve your problem though. (sarcasm. do not attempt)