Well, there’s an artery near the armpit. In the shoulder it’s the Axillary, below the shoulder it becomes the Brachial. It’s the same artery, only the names were changed to confuse pre-med students. As I’ve said before, I’m not a doctor, but my advice would be, “don’t get shot there.”
I don’t know what bleed out times look like if that’s severed, but at a guess I’d say, “not long.” Probably under 120 seconds.