From the pictures it looks like mouth rot. When I first got into koi, I had many fish get this, and I still don't know why... I did everything I do now. haha. But, I will tell you that it will take off the top part of it's mouth, and it could stop there, however, it normally doesn't and it will deform the mouth shut to the point where it will not be able to eat.
My recommendation is to use Tricide-Neo Dip, as well as antibiotic food.
Mouth rot is commonly due to over crowding, and bacteria.
How big is your pond, water parameters, what are you feeding, and when was the last koi introduced?
I have had many problems when I first started with my koi, but I have noticed a significant change in their health simply by switching to more expensive food. I feed only BlackWater Food. Growth/Color/Gold
I get my medicated antibiotic food off Dr.foster and Smith. It's made from BlackWater, which is one of the bed American Koi breeding farms in the country.
http://www.fosterandsmithaquatics.com/product/prod_display.cfm?pcatid=15912
And if you're serious about koi, I would go to
www.koiphen.com They have TONS of people dedicated to koi. They will be able to help you. Just be careful, sometimes people can be jerks on there.