The poem is an example of apostrophe, addressing Death (personified) as a living being who is thus listening to the speaker. This intentionally removes the mystery or sense of superiority in the concept of death, making it seem as though death can be easily defeated.
Allusion is used in the final line. 1 Corinthians 15:26 states, "The last enemy to be destroyed is death." This both echoes the sentiments of the poem, nothing that Death is the enemy of humanity, and that Death has no power itself. Ultimately, those who believe in Christ will defeat Death through salvation and eternal life. The speaker of this poem notes that death is simply a "short sleep," after which "we wake eternally / And death shall be no more."
A paradox is established in these lines:
For those whom thou think'st thou dost overthrow
Death thinks it it possible to "overthrow," or end the lives of, humanity. Another way to rephrase this would be "The people you think you have killed are not dead." This paradox reinforces the central meaning of the poem, that death has no ultimate power and is only a temporary transition into a much more powerful afterlife.
Caesura, which is an intentional pause within a line of poetry, is used in the opening:
Death, be not proud, though some have called thee
These pauses establish two purposes. First, the intended audience is made clear. It's a slow and intentional direct address, somewhat confrontational in nature because of the long pauses. Second, the central idea of the poem is presented in a pointed way. Death cannot call itself proud, and the speaker will provide the support for this statement throughout the poem. Caesura creates a dramatic opening for this poem, which one would expect when addressing Death itself.
All of these devices are used to achieve a nearly belittling tone toward death and therefore propel the ultimate message of hope in an eternal afterlife.