Given the placement of the radial artery in the wrist, I will add several thoughts:
1) If one is conscious enough to apply direct pressure, and one does so quickly enough, it's not unreasonable to survive this kind of injury; if you are briefly unconscious and so lose a fair amount of blood through radial artery bleed, it can be very challenging to stay fully conscious and keep applying direct pressure: as you weaken, and your BP drops, you become less and less well oriented to reality and concentration becomes much harder.
(If you are a polytrauma, you may well exsanguinate without care; a tourniquet may then save your life.)
2) If this device is in the wrist, and penetrates the radial artery, and the initial device-removing injury was essentially blunt-force trauma, there will also have been massive damage to the radial nerve which enervates the hand, both sensory and motor functions - especially the thumb and lower two fingers. As a direct result, one would expect your character to end up with ongoing neuropathy (might be only years long, or their whole life) ranging from tingles and lack of sensation to significant ongoing pain, grip strength waxing and waning, sensitivity to illness / infection which can result in temporary total dysfunction of the entire hand lasting a week or more and then slowly fading, and so on.
3) It's likely given the proximity of all these elements in the human wrist that the radius bone itself will have been at the least bruised or traumatized if not broken or shattered. This will add complications to all these considerations, as the wrist will need to be immobilized / splinted for some time.
4) The mental and emotional aspect of this is in fact quite daunting, as one then both goes through a long and arduous recovery process with a prognosis of severely limited recovery results, (say 50%-75% grip strength at best) and then must come to terms with the complete un reliability and un predictability of that hand in the long term: your character will occasionally drop thing that they were sure they had a good hold of, (bad proprioception nerve responses, bad sensory responses and bad motor nerve output) fumble things etc - and that's all after 3-6 months of total incapacity of that hand (think dead fish hanging off the arm the first 3 months) whilst they learn to use it again as though it were a newly-grafted on piece of flesh. During the time the hand is "coming back" and they are learning to use it again, it will feel almost completely numb except for excruciating bursts of pain and "fireball" feelings racing along nerve channels as individual nerve bundles get back to functioning; moreover, as the local nerve clusters have been scrambled, that relearning is not only hard, it's deeply disturbing - just imagine telling your little finger to curl as you always have, and having your ring finger straighten instead. It's as though the whole darn thing was... rewired. Randomly.
How do I know all this when I'm not a medical professional? Happened to me.
Link below is to a picture of that injury, on that day, in the ER - do NOT click on that link if you've a weak stomach.
gnarly picture of wound to radial area of wrist - don't click if weak stomached - really. Don't.