Who has the axe

Marking the stone to be dumped(k-d) should get rid of it, even it's not immediate.

You can also try to build a (C)floor at that square using that material, as that will usually just use that stone.

You can also designate to channel the tile the stone is sitting on then build a (C)floor over the hole.

If you actually mean a natural boulder above ground, then designate it to be smoothed.

EDIT: Nice pic. ;)

While JavadocMD's comment/answer may work. (Assuming you can have them kill it, if not you could still throw it in a deep pit.) This would usually result in mutilating the corpse, or maybe your dwarves would bury it.

The easiest and probably best way would be to train it as a war/hunting animal at the kennel. Then it will show up in the animal list and can be butchered.

As for why it won't normally show up, it's probably a bug related to the fact that you bought it.