since you can kill by cutting, it's hard to to disentangle the killing from the mere cutting.
An anecdote: in Italy you can often see the "scissors" hand gestures when the interlocutor wants you to get to the point. I don't know how ancient people came up with the word, but the killing metaphor seems a bit of a stretch; perhaps cutting one's tongue would be enough!
I did look it up, and the latin dictionaries give "fallen together" or "fallen into pieces", and it also seems to be used for slaughter. "With cuts" or "cut up".
Interestingly some etymologies give the original verb as concido (from cado, "fall", not "cut"). So the etymology of concisus (concise) could also be an expression of "squishing together".