Let's talk about the death penalty. All governments must answer the question of whether they have the authority to end the life of a criminal should the crime they committed be so heinous or so damaging that only the death of the perpetrator could bring proper catharsis and assurances to the community at large that the crime could not be repeated by that individual.
Here is a thought game to the moral quandary:
You are in a switching station to train tracks, a train is coming and unable to stop, there are two tracks, the track the train is currently on has 5 workers who are doing some routine maintenance and will not be able to get out of the way, on the auxiliary track there is only one worker who would not be able to get out of the way. Do you throw the switch, killing the one worker, in order to save the five?
Effectively you either allow 5 people to die, by not rescuing them, or you kill a man in order to rescue the 5. The death penalty works off that similar logic, let me modify this.
You are in a switching station to train tracks, a train is coming and unable to stop because a maniac disabled the breaks, and killed the engineer. There are two tracks, the track the train is currently on has a broken security camera so you can't tell whether the track is clear, but you know that track is due for maintenance; if the track is being serviced for maintenance then there will be workers present and they will not be able to get out of the way. On the auxiliary track there is only one person, the maniac. After killing the engineer he fled down the auxiliary track and will not be able to get out of the way of the train if you send it his way. Do you throw the switch, killing the one maniac, in order to save an unknown number of workers that the maniac put into danger having already killed an engineer?
Now substitute those potential maintenance workers with fellow prisoners, guards, psychiatrists, all of the people that might interact with the maniac, should you sacrifice them for the sake of the maniac? Is his life worth even the potential threat he posses to the hypothetical people now that he has already killed someone?
I say kill him.