Has he seen a psychologist? They can be very helpful at giving him an outlet to speak what is on his mind and to help him cope and manage his emotions. My son went to a counselor and it really helped him. He still has an anger problem but now he has better skills to manage it.
Good luck and I understand your frustration. However, I don't think giving him more chores to do is going to get to the root of the problem, although I think it's great at keeping him busy and there's nothing wrong with that. Still, there could be other things troubling him that are preventing him to be the best that he can be.
Has he been tested for ADD or ODD? I have Attention Deficit myself, so I've done a lot of research. Sometimes people with ADD or ADHD don't think before reacting and thus, say the most inappropriate thing -- even when it's not entirely what they mean. They then feel guilty and sorry for saying such outlandish things.
Edit: I just read your additional details and think that maybe you should take more drastic measures. Would you consider some type of boot camp or even a military school? My friend's son went to military school as a last chance thing, which I thought was really strange at the time. However, it turned him around one hundred percent and she said it was the best thing she could have done for him. He's went on to college, when before it wouldn't even have been an option.
I think those are extremely expensive. However, your son is so worth it and there is something more going on in his brain than he is able to tell you or that he even knows. Deep down I think he is crying out for some kind of help.
I really feel for you because I understand. My son had so many problems the first few years of his schooling. The principal was calling me two to three times a week and it made me just so sick. However, therapy has really helped my son and he's doing a lot better now. He still sometimes blurts out weird stuff but he controls himself so much more now.