The painting tells me a lot about myself and my biases.
I don't mean to make it sound like some sort of spiritual thing; it is not possible to have helped clean a carcass and still romanticize the practice of hunting. I explain it to substantiate this statement: the deer immortalized in that painting almost certainly died quickly, cleanly, and with a minimum of fear and pain. Of all the creatures likely to predate upon a quadruped herbivore, humans are the only ones who worry at all about that sort of thing, much less consider such outcomes worth effort to produce.
It speaks well of your kindness to sorrow at the death of a deer, and I don't mean to suggest that you shouldn't. But there are nuances here which are easy to overlook absent direct experience, and having seen them much closer to than many, I thought I'd take the time to explain a bit, in the hope that it might be of some little value to you.