These New Testament verses agree with Genesis 9 that human governmental authority derives from God. A purpose of human government is to keep chaos from developing. Paul does not specifically stipulate the extent of the wrath that human governments use to keep order, but his mention of "sword" indicates its use as an instrument of capital punishment.
Within God's purpose, "the wages of sin is death" (Romans 6:23). A person practicing sin earns death by his conduct. A difference between this and capital punishment is that God executes directly. Although He has given governments the authority to take life to preserve order—in conjunction with the testimony of at least two witnesses—He has never extended the same right to an individual.
God is the source of life, and He alone, or those to whom He delegates it, may take it. Of all of God's physical creations, only man has a mind capable of becoming like God's. God gave man dominion, but to rule properly requires character, wisdom, and understanding. The building of these requires experience, and gaining experience requires time.
Several of the Bible's writers comment on the brevity of a man's life. When a person's life ends prematurely by murder, or even accidentally, it at least interrupts, or in some cases, ends God's great gift. No puny man has the right to take it upon himself to interfere with the continuation of God's great gift to another. If a man does this, he will pay a terrible price.
Capital punishment, consistently and fairly administered, will deter murder. However, capital punishment is an after-the-fact deterrent. Jesus preached a much more effective deterrent in His Sermon on the Mount:
You have heard that it was said to those of old, "You shall not murder," and whoever murders will be in danger of the judgment. But I say to you that whoever is angry with his brother without a cause shall be in danger of the judgment. And whoever says to his brother, "Raca!" shall be in danger of the council. But whoever says, "You fool!" shall be in danger of hell fire. (Matthew 5:21-22)
It is essential to understand that Jesus did not do away with laws, but brought to completion the laws that already existed. Likewise, He did not do away with the Old Testament death penalty principles, which act as guides to civil governments. Jesus was a pioneer, not a revolutionary. A revolutionary seeks to destroy the existing order and places himself above conventional standards. A pioneer accepts the restraints laid upon him and moves forward.
Men's governments deal with the end of the act, Christ deals with the beginning. Jesus changed the law's restraint from the act to the motive. For the Christian, merely abstaining from the act is not sufficient. Jesus imposes the positive obligation of the spirit of the law on him. He seeks to prevent crimes of violence by rooting out the attitudes and drives in a person's character that make him kill. The New Covenant law searches the heart without doing away with the Old Covenant letter.