John Stewart Mill's View

Mill explains that "There is not, I should think, any human infliction which makes an impression on the imagination so entirely out of proportion to its real severity as the punishment of death."  He also says "When there has been brought home to any one, by conclusive evidence, the greatest crime known to the law; and when the attendant circumstances suggest no palliation of the guilt, no hope that the culprit may even yet not be unworthy to live among mankind, nothing to make it probable that the crime was an exception to his general character rather than a consequence of it, then I confess it appears to me that to deprive the criminal of the life of which he has proved himself to be unworthy--solemnly to blot him out from the fellowship of mankind and from the catalogue of the living--is the most appropriate as it is certainly the most impressive, mode in which society can attach to so great a crime the penal consequences which for the security of life it is indispensable to annex to it."
In short--Mills believes that when a person commits a crime so great as murder with no evidence to suggest that it was necessary/could be somewhat pardoned, the death penalty is a punishment which he sees fit.  "...the most appropriate as it is certainly the most impressive..."

To force someone to cease to live, to exist, because of their horrific actions, is a justifiable punishment according to Mills.