[Edited by AuguPerez114 on Sep 04, 2021]
With regard to Oxford and Cambridge, as their LLM and MSc programs have a more academic approach, applicants are required to have a first-class or strong upper second-class undergraduate degree with honors, which means that on the American scale a GPA of 3.7 out of 4.0 is required, while on the latin american scale, a 9.0 out of 10 is needed, so in these cases, I think you would not meet the necessary requirement to even apply.
As for the LLM programs from american universities, they normally do not tend to require applicants a minimum GPA.
However, take into account that the first aspects that universities see in the applications are the academic records of applicants, considering their GPA, as well as their class ranks. Even though that alone does not grants admission, it is the first step that puts one on track to be considered. Think that in highly competitive universities, such GPA may mean a competitive disadvantage when compared to other applicants who, only from Latin America, hold very high GPAs and are within the top 5% of their classes.
However, I would not suggest you to get disappointed. In Latin America, the academic quality among universities varies too much. So there are universities in which getting a GPA of 10 is nothing in comparison to an 8.0 from other universities. American universities have experience on this issue and take their admission decisions considering this aspect.
Now, as you asked for Harvard, being myself mexican who knows other mexican students who have been admitted to the LLM program, I can tell you that none of them had a GPA lower than 9.5. So even though Harvard states that they admit their LLM students based on an holistic approach, the reality or at least from what I have experienced, is that a strong academic record is extremely important if not essential.
[Edited by Guillermo Carrillo Duarte on Sep 02, 2021]
Article Mar 15, 2018
Having a stellar GPA may not be the only factor that will get you into a top LL.M. program.