I particularly enjoyed this poem, because it kind of reminded me of one of the major themes in Harry Potter: defeating death. In Harry Potter, Voldemort sees defeating death as literally never dying. Harry, on the other hand, does not give death this power by accepting his death, and therefore is more of a conqueror of death than Voldemort.
Anyway, the irony that the speaker of this poem creates is in the proposition that defeating death entails actually dying. "One short sleep passed, we wake eternally,/ And death shall be no more; death, thou shalt die."
I also noted that the speaker seems to have a vested interest in the subject matter of the poem; he seems defiant and passionate. This tone is created by the direct address to death ("death, thou shalt die") and also the speaker's mention of himself, and the denial that "nor yet canst thou kill me."