The climax of "Jabberwocky" is violent indeed – a hallmark of the "epic ballad" form, of which this poem is a tiny sample. The warnings in the second stanza of the poem set up the danger, which is quickly followed up by the protagonist heading directly off to rid the forest of the wild and unseemly creatures that are described. Not only does the hero vanquish the most fearsome of his foes, but he also beheads him, dragging the bloody thing back in order to prove his might to his father. The violence here plays to our desire for good to stomp evil right into the ground.
In "Jabberwocky," the violent dismembering of the Jabberwock is representative of a human desire to annihilate that which threatens us.
The battle in "Jabberwocky" is crucial in placing this poem among older, "epic" poems that typically glorify violent encounters.