This, according to the US Forest Service document entitled "Obliterating Animal Carcasses with Explosives," is the right way. See those rectangles? Those represent sticks of dynamite. Their placement demonstrates how they should be positioned in order to achieve what the document calls "total obliteration."

Pro-tip: The diagram up top illustrates how to explode a carcass when it needs to be eliminated quickly and absolutely. Under less urgent circumstances, the explosive placement illustrated below (corresponding to "partial obliteration") should suffice.

Pro-tip #2: In some cases, it is probably best to err on the side of caution and just go with wholesale vaporization, lest chunks of rotting animal remains rain down from on high.

For more details, visit the always-enlightening Improbable Research blog.