Dwarves will not use an item designated for dumping, ever. The only job they can do to it is haul it to a garbage pile.
Have you designated a garbage zone? Use (i), draw a square (1² is enough, it doesn't work like a stockpile. Consider reading a bit more about the advanced storage system that is the Quantum Stockpile, because a garbage dump functions essentially like a QSP), then use it as a (g)arbage dump. Make sure it is active and reachable by your dwarves.
Other things that might apply:
In your (o)rders menu, are dwarves allowed to gather refuse from outside? A rotting animal is refuse, which leads me to...
Butchers, cooks and tanners will not use rotting base materials for meat production, leather production or fat processing. You langur meat is lost
The items you wanted to get dumped may be forbidden! (d)-(b)-(c) to reclaim them.
Items dropped in the garbage dump are forbidden. Reclaim them.
