You can't just randomly stab your armpit and think you're going to hit an artery. You need to have pretty good knowledge of anatomy and even then everyone's anatomy is different. Also in order to cut it you'll have to reach across your own body and hope you get the angle correct.
Next, there is a risk of infection in your pit.
Finally this artery supplies blood to your arm. A failed attempt could lead to permanent nerve/muscle damage or amputation due to blood loss.
Cutting/stabbing is one of the least successful methods possible and the number of things that can go wrong is significantly high. I would not recommend it.