I have read numerous interpretations of this scene and generally speaking they're all quite interesting, but I believe it is our protagonist literally embracing death. Up until this point in the film, he has been running from the truth ("but I'm not dead") and in his vision quest for which his discovery of the fawn is a part, he finally understands Nobody(Gary Farmer)'s view that death is inherently a part of the fabric of life. In facing this truth, he finds peace and this scene perfectly illustrates this.
Aesthetically, the way the black and white film exaggerates the textures of the leaves, the fawn, the fur of Blake's coat, and the plaid of his trousers is rich and earthy. The appearance of his black hat in the top-down view of the scene is almost like a hole in the ground. Everything blends and in death, everything returns to the earth and in the stillness of this scene, it looks beautiful and tranquil.
The scene also reminds me personally of a time when my mum went mushroom picking in Washington State and one day found a mortally wounded deer in the forest. It had been shot and left. She stayed with it until it breathed its last and came home without the mushrooms but returned instead with a story. I was 10 years old at the time.
Dead Man trailer
Dead Man analysis (The Film Journal)
Jim Jarmusch Dead Man Q&A (NY Trash)
Jim Jarmusch (Senses of Cinema)
Jim Jarmusch Wiki
Jim Jarmusch interview (The Guardian)