I'm sorry, but these supposed solutions are absurd. Castration and amputation is not going to stop anyone from killing anyone else.
Why would destroying the means of a crime not reduce the chance of recidivism?
Consider also, Killing isn't generic. It has a context. People act out their ego identities. If one destroys the possibility of a violent or anti-social role to play, the individual will, hopefully, be forced to adopt something more pro-social.
Why are these solutions absurd? Why is rendering someone physically incapable of their crime of choice absurd? Granted, it's different, but is it less draconian than killing the felon, or locking him up for life?
And once you've destroyed their murderous mind/spirit, what point is there in keeping them alive, anyway? And if we did these things, I think we really would become as much a danger to our own society as they are.
So correcting the defect; the 'murderous mind', that causes the murder, renders life intolerable? I lack a murderous mind/spirit, but I never felt my life was pointless because of it.
We remove deleterious defects all the time: Tumors causing physical or psychological problems, abnormal pacing cells or pathways causing cardiac dysrythmias, &c.
If an overactive region in the brain is causing impulse control problems, or rage attacks, why not ablate that region? We do it all the time for seizure disorders. The patient would otherwise be unaffected, and grateful for the ability to maintain control and lead a normal life.