If you want them out of the way ASAP, just make a garbage stockpile outside (i-g) and dump the corpse (k-d), the dwarves seem to prioritize this over normal item hauling, so it should be done fast
And yet... It often isn't. Even if you change the inside/outside orders with "o" etc. They'll either prioritise it nice and fast, or they'll refuse to touch it, for years, until you get tired of it and wall it in years later, or the fort dies.
I've never had dumping not work, if it still isn't working, I would suggest forbidding then unforbidding it to see if it refreshes the dwarves noticing it....
Done that.
Also, I un-designated it for dumping, forbade it, unforbade it, tried it again. Also, I
A few years later the fort died of werebeast attack. I'm serious when I say that if Urist is going to go moody, and you don't have materials for his mood, don't let him take on a task. He'll never ever finish the task he was doing before he went moody. Also, dwarfs won't dump something someone else planned to dump before they died. It's ...sacred. Or at least that's what I decided it must be.
I understand why Urist wouldn't dump the !!reindeer!!cheese!!, or put it in a rubbish pile, or in a food pile for that matter, but after the smoke cleared and it was just a charred rotten reindeer cheese... it was annoying how it just kept on pumping out fumes, but still no one touched it, there at the foot of the stairs. After a full year (I decided to wait that long just in case) I walled it in. It continued to make smog in its own little room for years afterward.
The corpses... I guess they just had no living relatives or friends? I don't know. There were over 100 dorfs living in that fort. No one moved the corpses, even the one propping the door open, let alone the one rotting on the middle of the forge room floor. Then there was a werebeast attack and that was over in no time at all, so onward to a new fort...
Current one has a Xcat leather dressX which has been sitting in the middle of one of the entry hallways for six months or so now. I think everyone who walks past it just doesn't want the responsibility. It has a stockpile that could take it only six squares away. Go figure. I am about ready to start marking that one for dumping, but I don't need to: It doesn't make smells, like reindeer cheese does, so I'm less concerned.