Talk to the Hooded Figure in Rosenqueen and Introduce a monster to the dark world , then select the monster you want to get rid off (if you fully train a monster (and if you want to level them up a bit) you can get some nice items out of it, but if all you want to do is make a monster go away this is the place.

The other thing you can do is deliberately bring a monsters happiness right down to 0 with training and it will then flee ( I don't remember if you have to use it in battle with minimum happiness or if it automatically flees when it reaches minimum)

oh, thanks for the additional info