I don’t know. Misas beis din is meant to be a kapara. We can’t just kill people without a trial in beis din. I think that it is better that he be locked up tight in a cell by himself so that he can’t harm anyone ever again and let Hashem deal with him the way He wants.
I don’t say this out of mercy. I’m just not sure that we can kill someone or even put him in a position that he would be harmed without a beis din.