If you are a citizen and you can prove that the illegal alien married you because of your legal status in this country. THen your marriage would be consider dull under the grounds of defraudation of the state (which means one more charge against the illegal alien) and you will no longer be consider married to that person. Illegal immigration is a sensitive issue, make sure that you are firm in your resolution and that you are in your right mind when choosing to do whatever you choose to do.
An "Illegal Alien", why not just call them immigrants, or someone illegal, do they seriously look like aliens? Where's they're green skin, I wanna see. They're humans, like you. If you're married to them obviously the way a marriage ends is by divorce and it takes time.