I've only seen the movie-version of The Hunger Games, and have yet to read the books. Is it explained where the bodies of the dead Tributes go, if they are removed at all?
There was a guy like that a few years ago from District 6 called Titus. He went completely savage and the Gamemakers had to have him stunned with electric guns to collect the bodies of the players he'd killed before he ate them. There are no rules in the arena, but cannibalism doesn't play well with the Capitol audience, so they tried to head it off. There was some speculation that the avalanche that finally took Titus out was specifically engineered to ensure the victor was not a lunatic.
And on the hovercraft to retrieve bodies quickly:
Suddenly, the birds fall silent. Then one gives a high-pitched warning call. A single note. Just like the one Gale and I heard when the redheaded Avox girl was caught. High above the dying campfire a hovercraft materializes. A set of huge metal teeth drops down. Slowly, gently, the dead tribute girl is lifted into the hovercraft. Then it vanishes. The birds resume their song.
This may have been the same hovercraft:
After being picked up by hovercraft as described in @Solemnity's answer, the bodies get shipped back to the districts and the mourning families:
I have the pearl, though, secured in a parachute with the spile and the medicine at my waist. I hope it makes it back to District 12.
Surely my mother and Prim will know to return it to Peeta before they bury my body.
-- Catching Fire, end of chapter 25
Well, it is pretty clear overall from the books at least that the bodies in the first hunger games are picked up by hovercraft. However to more completely answer the question I would point out that Katniss thinks that the bodies of the tributes are revived (which would mean they would have to be retrieved quickly) and converted into the monsters she and Peeta have to face at the end.
...My head snaps from side to side as I examine the pack, taking in the various sizes and colors. The small one with the red coat and amber eyes…Foxface! And there, the ashen hair and hazel eyes of the boy from District 9 who died as we struggled for the backpack! And worst of all, the smallest mutt, with dark glossy fur, huge brown eyes and a collar that reads 11 in woven straw. Teeth bared in hatred....
So the mutts are likely the same tissue as existed in the tributes just revived and altered into a wolf. This is why she can recognize foxface (due to the hair).