Donne's first stanza argues to his beloved that, because the flea has sucked the blood of both him and his beloved, their bloods are mingled ('mingling bloods' is a euphemism for sex). Thus, because their bloods are already mingled because of the flea, she might as well have sex with him (which is the thing 'which thou deniest me').

The second stanza develops this argument: if the beloved marks the flea, and doesn't kill it, she'll spare three lives in one body (the speaker's, the beloved's and the flea's). Within the flea, the speaker argues, he and the beloved are "more than married", enclosed within the flea's body, rather exotically described as "living walls of jet".

But somewhere between stanzas 2 and 3, the beloved kills the flea: its innocent blood has "purpled" her nail. The speaker asks how the flea could be guilty, except in sucking the beloved's blood? Yet despite his protestations, the beloved is triumphant, and has killed the flea without damaging either the speaker or the beloved (as the speaker argued in stanza 2).

And (here's the twist) the speaker then argues that this displays how false fears are. He was scared that killing the flea would kill them both: and was wrong. And she is scared that sleeping with the beloved will dishonour her: and, as he was wrong to fear killing the flea, she must therefore be wrong to fear dishonour.

The argument isn't too persuasive, but you have to admire his pluck!