If you equate a person's rational choices with everything that comes out of their mouth, then you will euthanize a whole lot of mentally troubled or people.
I'm not even sure it's possible to divide the world between "mentally ill" and "mentally well". And if you could, I'd be inclined to say almost anyone who has been in serious chronic pain for years cannot possibly be considered "mentally well". Pain takes its own toll.
And dependimg the disease condition of the bipolar suferrer yes. Depending upon their stability which varies heavily from case to case and individual to individual. Would you want to do so at the peak of mania or the trough of depression, probably not.