In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner! May Allah bless you for this good question that reflects a sincere desire to know about the rulings of Islam and the wisdom behind its great guidance.
One of the basic Islamic rules in Shari`ah is that "no harm shall be inflicted or reciprocated". Hence, it is not allowed to kill a human soul in order to save the life of the other. Allah Almighty says: "And slay not the life which Allah hath forbidden save with right. Whoever is slain wrongfully, We have given power unto his heir, but let him not commit excess in slaying. Lo! He will be helped." (Al-Isra': 33).
As far as Siamese twins are concerned, if there is a possibility that both will survive, then it is not allowed to separate them. However, if the lives of both are at stake, there should be separation to save the life of one of them. Before carrying out the process, an honest and knowledgeable physician must examine the case and then decide whether or not to carry out the process and how it should be carried out.
Dear questioner, if you have any other questions, do not hesitate to write back.
