It is not impossible. However, effectively very difficult. The result would depend on various factors such as level of injury, and whether or not one of the major arteries of the neck are actually severed. If either the carotid or jugular is cut, you could die within minutes from blood loss, carotid also from CNS failure due to lack of blood flow to the brain, damage to the trachea could result in death from asphyxia. I can only imagine someone trying this in a situation of extreme desperation, it's most unnecessary and unreliable. For one, it is difficult to see the arteries yourself, many people survive neck wounds as they are imprecise. It is also incredibly difficult to fight your body's natural reflexes. So no you wouldn't be able to target two areas at the same time. It's most likely that after the first stab, if you even managed that, you'd be, in shock from the excruciating pain and terror and lack of breath, unable to remove the knife, which is the point you'd probably be found or get yourself to a hospital.
In short: in theory this could work, in reality most unlikely.