Strongly grounded in tradition, of course. The Church has always been in favour of the death penalty: history bears witness to this with one voice, both Church history and secular history, and where Church and saeculum coincide. However, it is no longer appropriate in a typical modern Western society, as the purpose of capital punishment is protection primarily, not retribution; ideally, in a society where prisons are common, even minimally economically viable, and used as a method of punishment (as opposed to holding prisoners for hanging alone), capital punishment is unjustified on these grounds alone, forbearing to mention the fact that human frailty in non-capital sentencing has less deleterious an effect (as innocent men can not be put to death, and it is great iniquity for innocent men to be judicially murdered).
Note, that I say “ideally”, because of human frailty (original sin, sin nature, etc.) in administering non-capital punishment is equal to that in administering capital punishment; it is that human frailty with the death penalty can not but help murdering some innocent men. The system should be designed to minimize the damage that human error and frailty can cause; and designing the system so that an innocent man can not be put to death is certainly minimizing the damage that human error can cause. Human frailty without the death penalty can release rapists, paedophiles, and other categories of almost-always-repeat-offender back in to the world.
This is not to say any penal system is perfect, or even close to it. But an ideal penal system and government should not have to use the death penalty except in extraordinary cases (emergencies, during war, military justice, etc.). For example, I am not opposed to the true life sentence (life without parole) for repeat offenders of such sort (most murderers are not repeat offenders); I am opposed to gaol sentences for drug offenders of pretty much any sort that didn’t commit any crime beyond using or selling the drugs; I am opposed to inequality in sentencing on race; I am opposed to serious criminals getting relatively light sentences, and junkies getting heavy ones - often heavier even in absolute numbers of years; etc.
To summarize, no penal system is perfect, but no imperfect penal system is helped to become more perfect by the use of capital punishment in the modern world, where capital punishment is too often used as a revenge, and not as a deterrent, protector, or rehabilitator; and almost all penal systems are helped to become more perfect by the lack of use or the removal of capital punishment.