You can read "yet" in the sense of "not yet." In this reading, the speaker doesn’t deny that death can kill; he only says that death can’t kill him right now. However, we prefer to read "yet" as a synonym for the word "even." The two words are interchangeable in this context during the Renaissance. So, Donne sticks his tongue out at death and says, "You can’t even kill little ole’ me, Death."
then from thee much more must flow (line 6)
We’re not so sure about the speaker’s reasoning here. How does he know that death is like sleep? Because people stay in one place with their eyes closed in both states? He uses their similarity in appearance to predict a similarity in their effect.
And soonest our best men with thee do go, (line 7)
This seems like a more reasonable basis for hope. People tend to base their behavior and beliefs on other people whom they really respect and admire. So, if good people act unafraid of death – either in war or in martyrdom – then, maybe they know something that the rest of us don’t.
One short sleep past, we wake eternally (line 13)
At the end of the poem, the speaker suddenly shifts into the future, imagining the time after the Day of Judgment when Christ "wakes up" the faithful Christians who died to join him in Heaven. This rhetorical move allows him to end on a triumphant note.