Is my PhD programme a scam? Does my department only want to get PhD students as TAs for their recitation section? Next month (August) I am supposed to go back to the US to continue my math PhD programme in a Public State University. I hold a TA position as everybody does in my department. Nobody, I say again, nobody holds an RA position. My duties, as equal to almost everyone, are two recitation sections of 60 students each. Every section meets 3 hours a week, that is 6 hours a week for both, plus preparing material, grading a weekly quiz (120 for both) plus grading homework weekly (120) plus grading classwork weekly (120) plus holding office hours plus organizing and keeping grade records plus going 4 hours a week to a center called "math help room".

I saw many US students leave the programme. They get fed up. The vast majority of the students are Chinese and they seem happy with it but I do not. The workload is too heavy and there isn't much time for learning or research. I have seen most people get their PhD at my department with only one publication that even says "to appear" on the resume of the PhD graduates. All advanced PhD students at my department spend even more of their time on TA duties than doing their research, as opposed to my country (Mexico) where advanced PhD students do not have TA duties.

Is that normal? Is my math department a scam?

I was surprised and happy at first that I was accepted to a US university to do a math PhD. But I could not get admission to a PhD in my country nor Spain nor Brazil, which are not supposed to be as good as a US university. Is my reasoning ok? Why did my department accept me when lower schools rejected me? Do they only want to get staff for their recitation sections?

Is my reasoning correct? Or is the main objective of a PhD here in the US just teaching?
The idea that there is some sort of dichotomy between academic mathematics "research" and "teaching" in the U.S. is an incorrect over-simplification. It is true that there is considerable PR hype about "research" being the fundamental goal/criterion/status-generator... It is true that almost all math grad students in the U.S. are supported as TAs, not RAs. It is also true that sometimes the TA workload is unreasonable, and, often, people seem to find the TA work more immediately gratifying than their research, and if done inefficiently certainly takes more than 20 hours per week.

It is also true that some grad students from abroad are happy enough to be in the U.S. that working conditions are not an issue...

While it may be that many academic math jobs, particularly those with lighter teaching duties, are filtered on research, faculty still inevitably spend quite a bit of time on teaching and service. If teaching is extremely unpalatable, then academic math will be unpalatable. 

Some people might say that any situation in which the "apprentices" cannot expect to get as good a job as the "master" are scams... but it's hard to find a situation in real life which works differently, I think. It's only a scam if someone makes a stupid promise to you that you'll eventually have a job just like your advisor, since, based on numbers alone, that's unlikely.

In my opinion, the true goals of graduate education in math are several: learn how to be an effective undergrad teacher, learn some advanced mathematics, learn how mathematicians make new mathematics, and practice attempting that.

In particular, research in mathematics requires mastery of so much prior work that it's very unusual for grad students to have genuine publications prior to the award of the PhD. This is very unlike lab-oriented engineering or CompSci degrees. That fact is not a sign of failure. If anything, it might be a sign of substance, that faculty insist on graduate education and more genuine research accomplishment than "papers" per se.

Also, in particular, again, the purported dichtomy between "researcher" and "lecturer", and a perception that the "goal" of graduate programs is to produce one or the other, is inaccurate. Graduate programs teach advanced mathematics to the grad students, and show what research is. The likely fact that they'll be doing a lot of teaching in their subsequent career does not affect the advanced mathematics... and the TA practice is helpful in becoming efficient and effective as a teacher.

There is sometimes a subtler issue, of grad programs which recruit international grad students who won't complain ... about workloads or anything else. That's not a good sign... but "even" domestic students are often pessimistic about the possibilities of change, and don't want to speak up for fear of retribution, etc. In the range of "generally reasonable", there are extremes, and there are abuses, indeed. Nevertheless, even then, it's probably not really a "scam".