A couple of years ago I was fishing in the boonies when I slipped on a slick rock and cut an artery in my knee. The flow of blood impressed me. I had a good 1st aid kit in my truck that had an Ace bandage and several gauze pads included. No matter how tight the Ace was wrapped the bleeding would not even slow. I tried using a tourniquet around my thigh but never successfully stopped the bleeding.
Fortunately it was a small enough artery that I made it to an ER where the Doc. had to open up the wound so he could get a hemostat on the artery.
Bottom line: If you cut a major artery you are probably toast. JMHO