The death penalty may be permissible when it is the only possible way to defend human lives. The Catechism of the Catholic Church explains:

Assuming that the guilty party’s identity and responsibility have been fully determined, the traditional teaching of the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor.

If, however, non-lethal means are sufficient to defend and protect people’s safety from the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common good and more in conformity with the dignity of the human person.

Today, in fact, as a consequence of the possibilities which the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm—without definitively taking away from him the possibility of redeeming himself—the cases in which the execution of the offender is an absolute necessity are very rare, if not practically nonexistent. (CCC 2267)

The death penalty did not make the list because it does not involve something intrinsically evil. If that were the case, then the Church would not permit recourse to the death penalty under any circumstances. Instead, we read in the Catechism the following:

The traditional teaching of the Church does not exclude, presupposing full ascertainment of the identity and responsibility of the offender, recourse to the death penalty, when this is the only practicable way to defend the lives of human beings effectively against the aggressor.

If, instead, bloodless means are sufficient to defend against the aggressor and to protect the safety of persons, public authority should limit itself to such means, because they better correspond to the concrete conditions of the common good and are more in conformity to the dignity of the human person.

Today, in fact, given the means at the state’s disposal to effectively repress crime by rendering inoffensive the one who has committed it, without depriving him definitively of the possibility of redeeming himself, cases of absolute necessity for suppression of the offender today . . . are very rare, if not practically non-existent. (CCC 2267)

The statement that recourse to the death penalty today should be "very rare, if not practically non-existent," is a matter of prudential judgment (cf. Evangelium Vitae 56).

Let’s first define what the Church’s teaching on the death penalty is.

The Church continues to uphold its traditional teaching that the state has the right and duty to protect general society from violent offenders, including by means of the death penalty if non-lethal means are insufficient to protect lives in an individual case. What the Church strongly encourages today is that the state do all that it can to satisfy its duty to protect society through non-lethal means, which are in better conformity to the human dignity of the offender and prevent the state from growing callous and imprudent in its application of the death penalty. It also prevents society from developing the "hang ’em high!" attitude that is unfortunately all too prevalent in countries that permit widespread use of the death penalty.

As for scriptural support for the Church’s modern pastoral approach to the death penalty, we can look to God’s mercy on murderers such as Cain and King David (cf. Gn 4:1–16, 2 Sm 12) as examples of extending mercy to those who, by reason of their crimes, could justly have been put to death.