If one wants to use OT justice to salvage war and self-defense, they have a lot of explaining to do as far as upholding consistency with the severity of punishment we should mete out, why they don't advocate family revenge for manslaughter, and all sorts of other things we find in the OT that even just-war advocates think we shouldn't implement. What is the rationale for incorporating a civic law from a theocratic ancient Israel despite seemingly clear teachings in the NT that this civic law doesn't apply in the new Kingdom? Yes, the moral law is immutable, but the sacrificial and civic laws were structures used to convey aspects of the moral law prior to God's perfect revelation in Jesus. Under Christ and the NT, how is capital punishment a more accurate vehicle to convey the New Covenant and the moral law as understood through the revelation of God in Christ Jesus?
It is this last part that is really the most important. Colossians and Hebrews are two books that emphasize the perfection of Christ's representation of God. Yes, God did reveal his justice in the Old Testament at times. But now, we have a better revelation. It's better than the angels, the prophets, the Torah, and all previous revelation, as Hebrews argues. We have the image of God himself. And what has that image revealed? The image has revealed self-sacrificial enemy love. If you want to argue that this aspect isn't a reflection of God and is only a role Christ filled to become the Messiah, than what hope do we have, those who were once at enmity with God? No, we love God because he first loved us, while we were still his enemies. The enemy love of Christ is prescriptive. He is the perfect revelation of God.
More than this new vs. old revelation (or complete vs. incomplete), those who want to use the OT to back up claims for modern violence have to move beyond explaining "just" violence for civic punishments. Most modern Christians who are not pacifists cling to a notion of just war. A just war values the preservation of civilians, yet we see the slaughtering of civilians in the OT. We also see some more gruesome features of war that don't seem to be condemned (e.g. David cutting off Goliath's head and its symbol of victory and taking it about the land). Most just war advocates will argue that this type of warfare was only intended for a theocracy where God directly commanded individuals, or that the more crude aspects of wars weren't directed by God, but were rather faults in the culture that God was patient with (akin to his permissiveness towards divorce due to the hardness of the peoples' hearts). But this is the exact argument pacifists make. It's just that rather than claiming we need a direct command from God to slaughter civilians, we need a direct command to do any violence whatsoever. I would argue that violence in general fits into Kierkegaard's "teleological suspension of the ethical."
Finally, it's interesting that God's reasoning behind preventing David from building God's temple is that David had shed too much blood. God wanted to be associated with Solomon, a man of peace. Even though David, a man who had done what God directed, was prevented from building God's dwelling place because he had killed (this is very fitting with the Orthodox theology, by the way, as they prevent anyone who has killed with religious leadership). In the New Testament, believers are the temple of God. We are his dwelling place. It makes sense that a God who wants to be known as a God of peace and who revealed himself in the Prince of Peace would not want his dwelling place to be marred by war.
[Edit: Tim Mackie from the Bible project has some fascinating things to say about God and his relationship to death. He clearly shows how in about 80-90% of instances where we think God is killing in the OT, that killing gets attributed to something else (natural consequences, an evil spirit being, etc). Similarly to Joseph's attribution to the evil of his enslavement to his brothers, but the good brought out of his enslavement to the purposes and hand of God - or how Jesus was crucified by evil men, but also by God's decree - so Mackie argues it may be with God's consequence of death. A God of life may actually not have so much to do with death as we think. Check out his podcast transcript towards the bottom of this link, or take a look at the document below.]