As virtuous men pass mildly away, And whisper to their souls to go,
Bummer. Folks are dying. In this case, the speaker is talking about the death of "virtuous" men, who "pass mildly away" because they have no regrets or shame. Death, for these men, is peaceful. So, maybe it's not such a bummer.
More than that, they are in control. They can simply "whisper" their souls away off to heaven. A little morbid, sure, but it's kind of nice.
The long vowel sounds like the U in "virtuous," the A in "away," and the O in "souls" and "go" make the lines long and breathy to say, even though they have the same meter as the rest of the poem (check out "Form and Meter" for more on that stuff). "Whisper" is also a sneaky onomatopoeia—the "wh" makes a soft, whispering sound.
Whilst some of their sad friends do say, The breath goes now, and some say, No:
Lines 3-4 tell us that, when these virtuous men die peacefully, all their friends gather around the deathbed. Sure, they're sad, but it also gets a little boring just sitting around and, you know, waiting on death. So they spend their time debating—one of them looks at the man in the bed and says, "He stopped breathing!" But then everyone else leans in and shake their heads, "No." I mean, it's the seventeenth century, people—it's not like he's hooked up to a heart monitor.
Whether or not this is the sort of thing that actually happened around a deathbed, Donne's really just emphasizing the point he already made. It's like a joke:
"Virtuous men die really peacefully."
"How peacefully do they die?"
"They die so peacefully that even their friends can't tell when they've checked out!"