"Death, be not proud, though some have called thee Mighty and dreadful, for thou art not so;"
Here, Donne personifies death. Donne removes power from death. He claims that it is not as "Mighty and Dreadful" as one might presume. By including the word "dreadful" implies that people have a fear of death. This is how a bully works: off of fear. Donne pays homage to the fact that "Death" is fueled the people's fear. Mankind is paralyzed by our conception of death. However, Donne basically puts puts "Death" in its place with the remaining lines. A reality check if you will!
"For those whom thou think'st thou dost overthrow Die not, poor Death, nor yet canst thou kill me."
Donne claims that Death cannot kill him. Death may think it is invincible, but Donne explains that those who Death thinks he has power over, he truly does not. In fact, those same people that do not give way to Death's power don't die. This does not mean they are immortal! Just wait Donne will explain how this works. Be patient!
"And soonest our best men with thee do go, Rest of their bones, and soul's delivery."
Yes, people do die. Death is a natural process in the human life. Even so, death is not selective. Everyone experiences death at some point. However, a clue to which Donne begins to hint at here is that death is essentially the resting place of their bones before their "soul's delivery." This is not Pizza Hut, Donne means the delivery of one's soul to the Afterlife or to Heaven
"Thou art slave to fate, chance, kings, and desperate men, And dost with poison, war, and sickness dwell, And poppy or charms can make us sleep as well"
This is a really interesting part in the poem because Donne solidifies his argument that Death is, in reality, a lot weaker than one would imagine. Death comes about only at the whim of kings when they sentence someone to death. Or when someone is fated to die on a certain day. Death has no say in the bargain. Chance also owns Death in that Death cannot control if someone falls off a cliff. Someone must slip and fall for Death to come about. The sequential order of events is inevitably out of Death's control. Other factors to which Death's power is removed are poison, war, sickness, and drugs; each evoke Death by their terms and not by Death's.
"And better than thy stroke; why swell'st thou then?"
Modern day translation: why are you flexing? Donne essentially threw several punches at Death in the last few lines. Here, we can imagine that is Death and Donne were two boxers in a ring, Donne has just done severe damage to his opponent. Unable o get up, Death is laying on the ground as Donne barks, "why swell'st thou then?"
"One short sleep past, we wake eternally And death shall be no more; Death, thou shalt die."
Death is simply a stepping stone before eternal life. While life on Earth may end at death. Death also marks the beginning of the Afterlife. While may be considered as a dead end road-Donne paints the picture that it is not. Thus, the idea of death and its power is meaninglessness. So basically what you just witnessed is Donne killing death. He really just did that.