It really doesn't matter which critter dined on your vine.  Whether it will survive depends on how deep the damage is.  I can't tell from the photo if it is girdled all the way around.  If so, that is a problem.  There isn't anything you can paint on it to repair the damage.  Just let it air dry.  I wouldn't do any cutting at this point.  Wait and see is the best advice I can give you.  If the damage is superficial, it will survive.  If it is deep and all the way around, your vine will die shortly after it leafs out using stored energy.  If that happens you may see new sprouts coming from below the damaged area and then you could cut off the dead vine above it.  I feel your pain.  Rabbits completely ate about three feet of my Strawberries and Cream honeysuckle.  The vine on the fence is just waving in the wind.  I also am hoping for sprouts from the stump.

The bark is removed from about 2/3 of the diameter of the plant so there is some left. As for how deep it goes I would say on the left side it’s cut in by at least 1/4”. 

I forgot to ask, so you think even if the plant is done for above that mark it will still probably sprout out and survive? Does growth that results from cutting the trunk tend to grow faster considering there’s a 10 year old root system feeding it?

It already has an established root system so that is a big advantage.  However, do not cut anything off until you see how well it responds to the damage.  It may just be that part of the vine will suffer were there is deeper damage.  Have a good summer and good luck.