Let’s look at passages on violence:
Ex 21:12, Lev 24:17, 24:21- man causing to smite human vitality shall be caused to die
Ex 21:13, Num 35:11 - man who didn't intend to kill shall flee to city of asylum
Ex 21:15 - one causing to smite parents shall be caused to die
Ex 22:2 - if thief is caused to be smitten to death in breaking-in at night, no bloods to him (presumably no responsibility for his death)
Ex 21:18-19 - man causing to smite man but does not deliver lethal blow shall compensate the victim for his injury
Ex 21:20-21 - man causing to smite servant with stick shall be at fault if the blow is immediately lethal, but not if death comes later
Ex 21:26-27 - man causing to smite eye or tooth shall set the servant free
Num 25:14 - Phineas caused to smite the Midianitess and the Israelite man
Num 25:17 - cause to smite the Midianites
Num 35:30 - all one causing to smite vitality/soul shall be murdered on mouth of two or three witnesses
One pattern I noticed was the phrase "cause to smite (yakeh) vitality/soul (nephesh)". This seems to mean to kill in its most basic sense, at least. Smiting or "causing to smite" by itself doesn't always seem to mean lethal blows. For example, Balaam smote his donkey repeatedly (Num 22:28, etc), and many of the passages specify smiting vitality or smiting resulting in death (though not all, such as the parents one).
Separately, there's the issue of "murder" (Ex 20:13 - you shall not murder, or "lo tirtsach"), and we also have the avenger of blood "shall murder the murderer, is-no blood to him" (Num 35:27).
Also, there's the passage that's been cited a few times recently (Ex 32:26-27) regarding the Levites killing their brothers and fellows.
So, what I've been wondering about is how to reconcile or otherwise think about these passages that at face value might be taken to be contradictory. Are there implicit and explicit exceptions to these rules regarding not murdering or not smiting vitality? For example, there is probably no debate that the Amalekites and Canaanites are to be completely destroyed (i.e., killed) by Israel, and it would seem to be indicated that warfare is allowed (especially in Deuteronomy which even says that voluntary war is permitted), although we are clearly told that we are not to murder in general and not to cause to smite vitality of human. What is the distinction between these things? Are these foreign peoples simply not "human"? I doubt that because we also have examples of it being acceptable or commanded to kill Israelite apostates, for example (not just in court judgment either, see Phineas and also the gold calf). Is warfare different somehow than just causing to smite someone in general, and if so, what would even define warfare? I question that because Phineas clearly took it upon himself to enact violence against the Midianite woman and the man involved with her; it wasn't until afterward that the people were told to go to war with them (I use the Phineas example because it is clearly indicated by God in the passage that it was a righteous thing that he did). Was "cause to smite the Midianites" not intended to be the causing to smite human soul/vitality? I doubt that as well (Num 31:7 - they killed every male, and 31:15 Moses was upset that they left the women alive).
Finally, what I wonder about in a practical sense are the boundaries of self-defense. It is explicitly clear that if someone breaks into a person's home at night that the person can smite the intruder with impunity. However, what about in other situations?
Smiting someone in general, except for parents, would seem to be acceptable so long as it is not to death, but in a self-defense situation where one is actually facing someone who very much intends to kill, it would likely be very impractical to try to simply incapacitate the person (even the use of fists, etc, can result in death). Would this fall under the city of refuge type judgment? I would doubt it because Phineas obviously wasn't expected to do that (and he obviously intended to kill), and also we would have to get into debating over what the meaning of "he willed not"/”hunted not” to kill implies.
I would like to find an actual textual justification rather than purely logical.
My first guess would be that this is an issue of translation. Word "smite" may not mean in Hebrew the same thing it means in English.
For example, in Russian we do not have the word "murder". Only "kill". So when I was translating the 10 commandments, i had to specify that it is only "killing with evil intent" that is prohibited. All other forms of killing are allowed. Even accidental murder is not considered killing under some circumstances (think asylum cities)...
The word "smite" (nawkaw) seem to have a general meaning of violence as it is associated with all three cases - striking, killing and murder so I think it needs to be interpreted as such. I do not think it would be possible to reconcile the meanings of the passages in English. Like I said above, I think it's a translation issue and in Hebrew all passages make sense.
One specific passage that I can recommend is Exodus 2:11-14. This passage can be interpreted both ways so it makes me wonder if Moses was a murderer? I do not think so because when I read "smite" in this passage I see it as Moses just incapacitating the Mitzri without actually killing him. This makes him an accidental murderer so he has to flee to Midian. I do not think that God would allow a murderer to lead His people, right?
As far as self-defense/intruders, Torah seem to be perfectly clear that you can kill them if they are threatening your life. Yes, there are not too many explicit passages about this but I think any normal person would understand it without any explanation from the text.
For example, my understanding Exodus 22:1-4 is that only a thief is exempt from being killed if the sun was upon him. Torah speaks specifically of a thief. If it is an armed robber then you can kill him at any time on your property (day or night). The issue seem to be of intent and tools with which a perpetrator is armed with.
And as far a warfare goes, Torah does not seem to imply aggression as we were to be priests to the nations, not their conquers. So warfare is allowed only against specifically mentioned nations (i.e Amalek, Cannanites) and for self-defense reasons imho.
Once again, I always check 10 commandments and see what they say. In this case, evil intent is what seem to be the difference between these words and passages.
Sometimes you have to be fluent in the language in order to understand the nuances of particular words and their meaning. Like I said, perhaps in Hebrew this word has slightly different meaning from "smite" so all passages make sense. Like difference between killing and murder in English.
See, say, Deut 19:19, 19:21. Intent is the key. So to me it's clear that if someone wants to murder me (or I have a Torah reason to believe so) I can defend myself with equal violence... Not everything is said explicitly in the Torah so you have to use logic to figure it out. Just because there are no textual passages does not mean it is not right thing to do. It is similar to the mushrooms issue as Torah does not say anything either way about it...
One other thought I had is that the reason it says "murder murderer" in Numbers 35:27 and 35:30 is because of "an eye for an eye" concept defined in Exodus 21:22-25 and Leviticus 24:19-20. Similarly in these verses Torah wants to say "murder for murder" as redeemer of blood is allowed to murder the murderer without a due process and in hate.
So perhaps the 6th commandment(not you shall murder) should be translated as "not you shall murder unlawfully" or "not you shall murder at will". This way it would say in Numb 35:27 "and murders at will redeemer of the blood the murderer at will". However, the seeming contradiction remains.