Surviving a cut to the Jugular Vein is possible if you're able to get the bleeding stopped soon enough and get medical attention soon enough as well.
The Jugular vein is very important because it drains deoxygenated blood from the head and the neck and without it and when you bleed out of it your body loses blood rapidly and cannot drain the blood back to where it's supposed to and instead it drains out.
So if you bleed from the Jugular vein and it's not stopped in time you can die soon after so it's very important to get medical attention right away.
Most people who do get a severe cut to the Jugular Vein die soon after but there have been a few people who have survived a cut to the Jugular Vein.
You will be very lucky if you do survive a Jugular cut but it is sometimes possible.
Most animals are rendered unconscious by cutting the Jugular vein first so that they die before they are slaughtered up.
So the Jugular Vein is very, very important and getting the Jugular Vein cut is a serious medical emergency.