"Elephant hunters in Africa, for example, often target the base of the trunk to cut arteries, causing the animal to bleed to death. The mammoth also had injuries to its jaw that suggest the tongue was cut out."

As a way to bleed it out.

I think that's the wrong interpretation by quite a ways. No hunter cut a tongue out to injure an animal so it would die (the purpose of the trunk thrusts). Nobody gets close enough to cut a tongue out without the animal being dead already.

An animal can fall and not die for many hours; the elephant might be incapacitated but not be dead.

Because to a modern, american reader it might be not normal to assume that the tongue is eaten?

Of course its eaten! That is the sole butcher mark mentioned in the article. Thus my original comment.