The first line of "Absent from thee" makes it seem as if this is going to be an old-school love poem. The speaker begins with an apostrophe to his lover, telling her that, while he's away from her, he "languish[es]," practically wilting from his longing for her. So far, so familiar.
But the second line abruptly changes course. "Knowing that I long for you when I'm away," the speaker basically goes on, "can you please stop bugging me about when I'm going to come back?"
It's not just the meaning of this question that feels like an abrupt change, but the sound. Listen to the way consonance works in these first two lines:
Absent from thee I languish still;
Then ask me not when I return.
The first line repeats languorous, liquid /l/ sounds; the second, on the other hand, is marked with crisp, curt /t/ sounds. It's as if the speaker moves speedily from flattering his lover to cutting her off.
Already, then, readers get the sense that this "love poem" isn't what it seems. This will be a poem, not about true love, but about the speaker's desire to have as much sex as he likes with whomever he likes.
His one problem is that his current girlfriend isn't so into that idea. As such, he'll communicate his real desires in the language of love poetry, framing his plans to sleep around as an expression of sincere affection for the lady he's addressing. This poem will be a satire of love poetry, and even of the clichéd "power of love" itself: love's power, this speaker will suggest, is no match for the force of lust.
The rest of this stanza shows exactly how the speaker will go about mocking the conventions of love and poetry. Having warned his girlfriend to stop asking him when he's coming back, he goes on to add that it would absolutely kill him to stay away from her any longer. But take another look: he doesn't exactly say that it would kill him to stay away, but that it would kill a hypothetical "straying fool"—that is, the sincere, devoted kind of lover he's mocking here.
He conceals that sly little moment in florid poetic language. Take a look at how he uses chiasmus in line 4 here:
The straying fool 'twill plainly kill
To wish all day, all night to mourn.
The flipped grammar there draws a lot of attention to itself—and makes it sound as if the speaker is putting on an elegant Poet Voice to deliver his insincere message of love. Watch out for that kind of dramatic, disingenuous poetic diction: this speaker is about to use it a lot.