Domestic Violence is specifically noted in the Immigration Laws and Regulation for severe treatment. However depending on your case and what is stated in your conviction there may be ways to prevent you from losing your green card and being removed or deported from the U.S.
It is very important to get certified copies of your court record and arrest report if you have been accused of any crime. A State Court Conviction can affect your green card and your right to remain in the United States. Immigration Laws focus on the actual action (wording of the law) that you are accused of as well as the wording of your conviction record. Having a conviction vacated or expunged will often not help you avoid deportation or removal from the U.S.
If you are in court proceedings now you should have a criminal attorney and should have your criminal attorney work with an immigration attorney to decide the best way to handle your case.
Please contact a licensed Immigration attorney before you act on your specific situation. Immigration Laws and Federal Regulations are constantly changing and the general information provided can change over time.