Each case is different, each physical connection is different, and each surgery is different. So it is a different shailah every time.
When one conjoined twin dies (if natural causes), the other may die as well. This is what reportedly happened with the famous “Siamese” twins Chang and Eng (who were not Siamese, BTW), for whom the condition of being conjoined was named. One of the brothers died, and several hours later, so did the surviving twin. This would tend to support the idea of the twin being a rodef, as the shared circulatory and respiratory system could have ramifications on both. I would think that if they were not joined except by a flap of cartilage, there would be no problem in halacha, with separating them.