The speaker in "To His Coy Mistress" employs wit in an attempt to convince his unnamed lady to engage in sexual relations with him. His message is seen as a carpe diem ("Seize the day") poem, urging her to become intimate with him because they don't actually have all the time in the world for her to procrastinate this decision. Instead of coming right out and saying so, the speaker crafts a witty persuasive speech to attempt to sway his lady's opinion.
One place where he uses wit is in the following lines:
And you should, if you please, refuse
Till the conversion of the Jews
If they had all the time in the world, she could refuse him until Jews converted to Christianity—which is fairly impossible. The speaker relies on religious imagery to persuade his lady to engage in immoral acts, which is a witty move.
There is also a witty connotation in the following:
My vegetable love should grow
Vaster than empires and more slow
Critics debate the meaning of "vegetable love," but one common interpretation is that the "vegetable" refers to a certain part of the male anatomy which is shaped like some vegetables. This is a pretty risque move, but it certainly shows great wit.
In one of his darker moments of wit, the speaker addresses his lady's virginity:
then worms shall try
That long-preserved virginity
His reasoning here is that she can't die a virgin. After all, if she doesn't have sex with him and then her life ends, the worms will take her virginity.
The speaker returns to the world of nature for another comparison:
And now, like amorous birds of prey
The speaker relies on the "birds and the bees" euphemism
to convey the need to mate. This witty move portrays sex as both a natural occurrence and something slightly dangerous with additional connotation associated with birds of prey
The speaker of this poem doesn't approach his lady with an entirely serious tone, so his pride is intact if she refuses. Instead, he uses hyperbole
and wit to construct his persuasive argument highlighting all the reasons that she should be intimate with him.