Not bearing the sword in vain

for he is God's servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain. For he is the servant of God, an avenger who carries out God's wrath on the wrongdoer (Rom 13:4).

This is a classic prooftext for capital punishment, but is that what it means? According to Ben Witherington:

But does "the sword" refer to the general functions of government, or is Paul already thinking more particularly about the tax police? I believe the reference to taxes in vv6-7 is just a pertinent illustration of the general principle that officials do have the right to use force. But it is unlikely that Paul has capital punishment in view, for which the weapon mentioned was not used. Romans practiced crucifixion, or beheading by a much more lethal weapon. B. Witherington, Paul's Letter to the Romans (Eerdmans 2004), 314.

Several issues:

i) Witherington is a pacifist, so that may bias his interpretation.  In fairness, proponents of the death penalty can have a bias in reverse. 

ii) The context involves the Roman magistrate punishing malefactors. The "sword" as a reference to capital punishment would be fitting in that setting.

iii) In addition, Paul already mentioned the sword in 8:35. There, the implied context is martyrdom, where Christians may face execution for their faith. Since it refers to capital punishment in that previous passage, this makes it more likely that it refers to capital punishment in 13:4.

iv) It may include capital punishment without singling out capital punishment. It may be a symbol or synecdoche for lethal force generally, such as how Rome forcibly responded to uprisings. 

v) Commenting on Rom 8:35, where the same Greek word is used Jewett says:

The climatic tribulation in Paul's catalogue is capital punishment, referred to here as machaira, the short sword or dagger opposed to the long sword. In Rev 13:10; Mt 10:34,38f.; Acts 12:2; Heb 11:34,37, this word refers to execution by the sword, the ultimate punishment of the state…And that the sword was regularly employed in Rome in the enforcement of its decreers, such as the Edict of Claudius, hardly needs to be recalled. R. Jewett, Romans (Fortress Press 2007), 547.

Whether or not the Greek word was the technical term for the kind of sword used to decapitate offenders, Jewett documents NT usage, where the word is employed in capital cases. 

vi) In sum, I think 13:4 probably covers capital punishment, although the sword may be applied more widely.