From INS Website:

You may lose your permanent resident status (green card) if you commit an act that makes you removable from the United States under the law, as described in Section 237 or 212 of the Immigration and Nationality Act (INA). If you commit such an act, you may be brought before an immigration court to determine your right to remain a permanent resident.

From Section 237 of the Immigration and Nationality Act:

“Any alien who at any time after admission is convicted of a crime of domestic violence, a crime of stalking, or a crime of child abuse, child neglect, or child abandonment is deportable.”

But that article is rather interesting:

The Woods case brings up the uncomfortable problem with the new domestic-violence laws, which is that strict gender equality often confounds common sense. It is impossible to imagine Tiger occupying the same cultural brain space as Rihanna, with Nordegren playing Chris Brown. If Tiger had been chasing down his wife with a golf club and she had shown up with bruises, even if she had cheated with, say, K-fed, we would be a lot less ambivalent and complacent. If Nordegren had then issued a statement calling her husband her courageous savior, we would be outraged and filled with disdain and pity. All of these gender-dependent reactions make some instinctive sense. But legally speaking, they are beside the point. The law no longer makes the distinction.