If I go to Mexico and we get married, can I bring him back to the US before the 10 years?

If he is barred from reentry for 10 years, it does not matter if you get married to him there. He is still barred from reentry for 10 years unless he can get a waiver of the bar to reentry.

I am afraid, if as it appears your boyfriend was deported from United States for making a false claim to US citizenship under s.212(a)(6) (C)(ii) INA, he may NEVER be eligible to get an immigrant visa to return to the US even if you marry him. False claim to US citizenship is one of the worst offenses a foreigner can be charged with. In fact, one immigration judge said compared the punishment to death a penalty). I do not have all the facts and this does not mean your case is hopeless. But before doing anything, you must consult with a competent immigration attorney to advise you of your options.

All Immigration questions are very fact intensive, and no easy answer can be given to your question without meeting with you in person and delving into your life history and what you might be eligible to apply for from USCIS.

If the charge is false claim to US citizenship than he is barred for life and there is no waiver. If he just has a 10 year bar there may be a waiver available. Speak with and retain an immigration attorney, feel free to contact my firm for more details.