The word "crime" conjures up images of jails, and suggests that the mistress should be, if she’s not already, locked up. As the poem continues, we see that the speaker sees her "crime" as both against herself, and him.
in thy marble vault (line 26)
The graveyard imagery is one thing that makes this more than just a love poem or a pick-up line. The marble vault represents what the speaker thinks his mistress has: a closed, limited way of thinking about the world. He thinks that she is trapped by her "old-fashioned" views on sex. Perhaps, it also represents the speaker’s closed-mindedness, too. He seems very convinced that his way is the best way.
And while thy willing soul transpires At every pore with instant fires (lines 35-36)
What beautiful lines. We see a body and soul act in harmony, and a body burn with freedom and joy. "Transpire" has a few fun meanings that you can chew on. The first is "to come to light." The second is "to happen." The third actually has to do with plants. If a plant "transpires," it loses water vapor through its stomata (little pores on the leaves), a crucial part of photosynthesis.
Now let us sport us while we may (line 37)
The speaker seems to say: we might not have all the time in the world, but we are still free to play. Sport and games are often associated with freedom. During World War II, one way that Americans show their support for the war is by indulging in their freedom to play baseball. The speaker, of course, is talking about sexual sport as freedom, or perhaps sexual freedom as sport.
Thorough [through] the iron gates of life (line 44)
Here, Marvell combines both freedom and confinement in the same line. He reminds us of the "crime" of the first stanza. It also states quite plainly that the speaker thinks life is a prison to escape. The speaker finally describes what he wants to happen – he wants to burst through the "iron gates" of the mistress’s "coyness." He wants to transform life into a free place.