Most Helpful Guy
The problem that you face here is not the name calling, it is his sudden explosion of rage.
It is not your fault, but you might have stepped on an old mine field. Deal with this carefully,
find out why he thinks that way (being angry with the racist part). Try to explain that you didn't mean to belittle him when you say that he is Mexican.
Hopefully it helps.1
Most Helpful Girl
You've only been together for 3 months. Honestly, I'd probably just break up with him.
Not only is name-calling really disrespectful, but if you date someone who has an explosive temper, you're going to fee like you have to constantly walk on eggshells, for fear that you may accidentally say the wrong thing.
I can understand that he's sensitive to what he perceived as racism. He's probably experienced racism throughout his life, and it's really awful that people have to deal with that. But it still doesn't justify his response. In a healthy relationship, if you feel hurt or insulted by your partner, you should talk to them calmly about how you feel and why and resolve it that way. While your comment doesn't seem racist to me, and I'm certain you didn't mean it that way, I assume that you care about him and would be willing to hear him out if he told you that it bothered him.
Anyway, if you do decide to stay in this relationship, in the very least, I think you need to have a conversation with him about, well, communication. For example, make it clear to him that name-calling isn't acceptable to you.1