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to mink who kill for the fun of it and leave a bloody trail of dead things every where they go. Everything has to eat and very little actually goes to waste

I'm pretty sure only man kills for the "fun" of it.
Fun is something that you need a human level of intelligence to seek.

Mink kill by biting the necks of their prey.
Sever the neck artery, your going to get a lot of blood.
Animals that we say are having "fun" are just responding to outside stimuli that trigger biological responses on their part.
You take a cat/ mink/ weasel etc and put them in cage with multiple prey animals darting about, they'll attack everything that moves because it's a natural response for them.

Same with wolfs / caribou.  The wolves are just maximizing their chances for a meal by attacking as many as they can, not knowing if the animal will drop or just be wounded and escape. It's obviously a inexact "science" and that's why they sometimes kill more than they can eat. But like you said, everything needs to eat and maybe that's Natures way to make sure every predator/scavenger in that food chain has a chance to survive.

That's why animal experts say never to turn and run when facing a dangerous animal. It just triggers even more aggressive behavior.

What we humans might see as just killing for "fun" has a instinct driven reason that we might not understand but they do.