In my opinion, the author uses both paradox and personification to emphasize the idea that, in the end, it is life that will triumph over death.
The idea that death can die is a paradox. By saying that this is possible, the author is making us think in a different way about our assumptions. By making us think about this, he makes it easier for us to accept his premise.
By personifying death, the author helps with his paradox. If death is human, then death must surely die.
So, the author is asking us to think about the idea that death can (through God) be "killed." He uses personification and paradox to make us consider this possibility.
"Death, be not proud" by John Donne is among his Holy Sonnets and should be read in the context of Christian theology concerning death. In this context, human death and mortality are consequences of original sin. Our death, however, is only physical. Within Donne's theological tradition, the human soul is immortal, and will, after the Last Judgement, be given eternal joy in Heaven or eternal torment in Hell. The Apocalypse and Last Judgement mark an end to human mortality, and thus the "death" of death; after this point, all humans shall exist as immortal souls in a purely spiritual realm and death shall no longer exist.
The key paradox presented in Donne's poem is this core Christian belief that death itself "lives" for only a limited historical period demarcated by Creation and Resurrection, while humans who appear mortal and ephemeral actually have souls that "live" far longer, something Donne emphasizes in the lines:
One short sleep past, we wake eternallyAnd death shall be no more; Death, thou shalt die.
Since Donne devoutly believed in the expectation of the Christian Resurrection, his poem personifies death as an adversary swollen with false pride and unworthy of being called "mighty and dreadful." This poem is one of his "Holy Sonnets," in which Donne sees Death as mere adversary and God as vanquisher. In "Death be not proud" the poet accuses death of being little more than a slave bossed around by "fate, chance, kings and desperate men"—a craven thing that keeps bad company, such as "poison, war, and sickness." Finally Donne taunts death with a paradox: "death, thou shalt die."