In the field this is presents a challenge. If the first responder can control bleeding (internal, external) until the patient is in the operating room, a good vascular surgeon can save this one, so it's not necessarily instantly nor universally fatal.
The answer to this question depends on the amount of blood loss. Complete severing of the subclavian, jugular or either inominate with no control whatsoever results in massive blood loss. I'd say you have max 1-3 minutes before mortality. However, anything that controls bleeding increases that time, and I would not say this injury 100% lethal.
Some of the factors invovled are: