Who performs this service, and what is done with the remains?
It completely depends on where you are. In a few areas you can have a large animal body removed for free. In some areas it can cost as much as a thousand dollars (completely outrageous)!
The costs that I’ve seen in WA, OR, and ID are between $80-$200.
If you don’t know who to call in your local area, call your Vetrinarian. They will be able to provide you with the names and phone numbers of people who do this service. The other poster is completely correct though. Usually the dead animal has to be located in a very convient spot for pickup. They will no longer drive into fields, to do this.
As to what they do with the body, that kind of depends. Why it died (contageous disease, or a broken leg), how fresh it is, and how it died (natural causes, bullet, or a Vetrinarian administered euthinasia).
The animals body might be turned into pet food if a factory is close (in something like the case of a broken leg, and bullet to the brain). Or into fertilizer (something like a contageous disease, Vet euthinasia, or not so fresh).
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I assume that you are talking about a dead animal. There are services that will come and pick up dead animals. They used to pay you a little bit for calling them. Then they would pick it up free, now you have to pay then around forty dollars to pick them up. You have to be there with the cash in hand and have them so many feet close to the road and about a dozen other rules before they pick them up. We have it to be cheaper and less trouble to call someone with a backhoe to bury them.