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The opening scene shows us the native were sorry to kill the animals but they neede to hunt to get food.
The Last of the Mohicans Movie
To add a more in-depth answer. The scene represents the Native American religion. As in everything, living or inanimate, is all part of the Great Spirit, and created by it. It is customary to ask for forgiveness when you take the life of an animal, whether you are hunting it for food, or defending yourself, because they are related to one another and it's the same thing as killing ones brother/sister. Meaning, they value the Elk they just shot, and apologised for killing it. I hope this answer was satisfactory.