Is it discrimination to hold someone from a minority or underprivileged background to the same academic standard as regular students?
You are asking two separate and completely unrelated questions. The first, which you posed in the title, concerns the meaning of the English word "discrimination". The answer to that question is very simple: no, treating all students according to uniform standards and policies without consideration of their membership in various ethnic or racial groups is not discrimination; rather, it is precisely the absence of discrimination. That says nothing about whether it is a good or a bad (or moral/immoral, ethical/unethical etc) policy, it simply answers the question of whether it fits the meaning of a particular word in the English language.

Your second question was about how graduate students from minority and/or underprivileged backgrounds "should" be treated, which I interpret as asking about whether the policy of applying uniform standards to all students alluded to above is a good or a bad thing to have. This is a special case of a large set of questions associated with the terms affirmative action and reverse discrimination. It is a controversial topic that has been and still remains the subject of a large amount of debate as well as litigation, and if you care to learn more about it, there's a large body of discourse on such questions that you can find referenced in the Wikipedia articles linked above or with a google search. It is a sufficiently complex topic that I feel I can't meaningfully comment on it in a short post, and in any case enough has been said about it by people who have given the subject much more thought than I have to make anything I can think of saying about it laughably simplistic and uninteresting.

To clarify, this answer expresses no opinion about what policies should be in place for treating graduate students from underprivileged backgrounds.