How we cite our quotes:
One, two! One, two! And through and through
The vorpal blade went snicker-snack! (17-18)
Finally, some actual, combat-style, hand-to-hand violence. This is all we get in the poem – we've got one more quote to come, but it's after the slaying. Perhaps because it was positioned as a book for children, the actual battle in "Jabberwocky" is nearly an afterthought. We have four swings of the blade, and the implication that the blade is going "through" something (which, if you use your imagination is probably pretty gross), and that's nearly it. We also have snicker-snack, the auditory clue that the sword is making contact with flesh. Again, if you use your imagination here, you could probably come up with something downright gory, but the poem isn't going to give it to you – it doesn't want to scare off its youngest readers.
He left it dead, and with its head
He went galumphing back. (19-20)
Thus ends our battle scene. With no evidence of struggle, we have to kind of imagine it, but the outcome is decisive indeed and that the Jabberwock is dead. (Things we don't know that are also interesting to contemplate: whether or not the protagonist was injured, how long the fight lasted, how exactly he killed the monster, etc.) Not only is it dead, but our hero beheads the thing. If you let your imagination do some work, this image is horrific. Again, given the genre of the poem (quasi-children's-lit), it probably isn't reasonable to expect Carroll to outline in gory detail every moment of this violent encounter. But nevertheless, the creature is not only killed, it's dismembered, and its head is almost literally brought back on a platter.