Under certain circumstances, stoning, capital punishment, cutting off of hands, etc. is permitted in Islam as punishment for certain crimes. I understand that there are many different criteria the crime must meet for the punishment to be applicable.
But why is violent punishment allowed at all in Islam? What is the justification behind it? If, in an Islamic State, you did not punish criminals in the way stated in the Hadith and as the Prophet did, would you be doing a wrond in the eyes of Allah?