For a Tytalus Necromancer, just remove the word "battle" from silveroak's post. 
And change "pointless" to either "impossible" or "hilariously easy" depending on the foresight of the Tytalus.
It's a theory but recall Hermetic Magic cannot affect the soul and therefore can't empirically confirm or deny this.
It doesn't seem to fit with Living Ghosts, who are certainly written up as retaining reason, intellect, and free will.
Of course characters wouldn't know for sure, but now I'm talking from a player's point of view (or rather, SG's). If I recall correctly, canon does state that in death the soul passes on, and only the spirit remains behind if a ghost is formed. But I'd have to look it up, because it could be me overlaying my own opinions on top of what I remember as RAW.
There is no cannon as to whether it is a soul, the spirit, a copy of the original, an echo or what exactly- that is left up to the GM's metaphysics. It is stated that the spirit of someone who is given a Christian burial cannot be summoned, and the whole soul/spirit dichotomy doesn't fit with the mainstream Christian theology of the time, which is generally presumed to be the truth in AM, despite the claims that it is not.
The soul is unknown/unknowable not just to individual characters but to the Order of Hermes as a whole. This makes me think it improbable that there would be a rule banning beings of Might because they're "soulless".
The souls of those given Divine burial rites are only protected from vanilla Hermetic Magic. According to Ancient Magic this is a flaw in Hermetic theory that is corrected by Canaanite necromancy.
There's a basis in late antique and medieval thought for a soul/spirit dichotomy but the game rules handle it in what seems to me to be an incoherent way. I like to think that the soul is beyond the scope of the game and its behavior or even existence unknowable.
Back to the original topic.
Could a ghost (for example a ghost warder) kills another ghost?
I know that some old battlefields have legions of ghosts replaying the battle every night or so.
But outside of this specific context - which looks more like a curse upon the poor spirits - what do you think would happen?
Let's take the Calebais setting.
One magus enters the fallen covenant, and got attacked by the ghost of a grog. The magus is a necromancer and he has a ghost bodyguard.
Could the ghost bodyguard slay the ghost grog? If so, would the ghost grog come back to "unlife" on the next day? Or would he be soundly killed, and thus let vis?
What do you think? 
I think it would depend on the nature of the ghost grog. Generally the only way to get the vis from a ghost in my understanding is to put it to rest, but situations and storyguides may vary...
I would personally have the ghost come back to "unlife" the next day, so it wouldn't really be "dead" and thus would not leave any vis behind. But that's only my interpretation, of course.
I'm with ... everyone else.
If two ghosts get into a fight and one 'dies', then the death is just a temporary thing and not an actual defeating of the spirit.
It's like two ghostly armies that clash every night. Next night they just do it again.
Though it might be better if they came back next Oct 31st/Nov 1st instead of the next night. Let the group feel like they have accomplished something...