How to convince my PhD advisor to keep working with me if I am switching university? I am in a low ranked US math PhD program. I generally get along well with my advisor and like my research area (complex algebraic geometry). But the objective of my PhD program is to get low paid math teachers. We are overloaded with TA assignments.

So, I could get into a foreign math PhD program in South America. I am starting next July. Those foreign institutions generally offer full scholarship through the their Federal Government without any duties, free tuition + living expenses. No Duties Attached.

The thing is that I want to keep working in collaboration with my current US advisor, but he got mad and upset when I told him I am moving to another university.

How could I convince him to keep working with me? I mean there is internet and Skype. But I have not talked to him since the time I told him I am moving abroad.
It sounds like you should probably not expect your advisor to continue as your advisor. In choosing to leave the program (and, indeed, the country), you have relieved him of responsibility.

Advising students is difficult and demanding work. It is much more difficult, and less rewarding (for both the advisor and the student), when done over correspondence. Usually when advisors agree to do this, some combination of the following two factors are in play: (1) the student is near the end of their Ph.D. studies (and already has a thesis problem); (2) the advisor left the university (either temporarily or permanently) and the student didn't want to or couldn't follow them.

I don't know your exact situation, but I would recommend looking for a new thesis advisor in your South American university, while still trying to salvage a productive relationship with your current advisor. Even if he is no longer willing to assume formal responsibility for advising your thesis, he might still be willing to suggest open problems to you, offer advice, or be supportive in other ways.

One course of action that might turn out well for you would be to investigate opportunities that will be available to you at your new university, and schedule an appointment to discuss with your old advisor which of them he thinks it would be most valuable to pursue. 

Good luck to you in any case.