First of all, as others have stated, the phrase is "supposed to," not "suppose to," but if you were saying it rather than writing it, it's doubtful there would be a discernible difference. Also, at least in the U.S., we graduate "from" a university, but I'm pretty sure that in the British television shows I watch, I hear them say "graduate university" all the time. (There are other examples of this, such as Brits going "to hospital" and Americans going "to the hospital.") Now, as to the major concern of all the other responders here (and probably the person who corrected you), in the strictest sense they are correct: If you say "I'm supposed to," it implies that there could be reason to doubt that you actually will. However, this phrase is in extremely common usage now, and I personally would not bother correcting you on it, especially in conversation. Here are some examples of its (mis)use that I hear ALL the time from native speakers: "Would you like to go to the movies tonight?" "Oh, rats! I'm supposed to go to a lecture at the university tonight." "Dinner was great! Should we order dessert?" "I'd like to, but I'm supposed to be watching my weight." "When do you finish college?" "I'm supposed to graduate in May." In my experience, native speakers, even the well-educated and grammar-aware ones, would just as likely say, "I'm supposed to graduate in May" as "I graduate in May."

You can also say: I hope /expect to graduate this year.

Your word choice suggests that there is a possibility that you might not graduate. This is always the case... You might break a leg or get sick - or a teacher may give you a bad grade, or more likely there may be a problem with your paper work. If you are being cautious because of these possibilities, you might say : "I should graduate this year." or "my graduation date is likely this year." or "I am scheduled to graduate this year." or "I will most likely graduate this year." You may also be bolder and say "I will be graduating this year." Whatever the reason you might not graduate this year, those are not your choice. Those are things not in your control. "Suppose to" often is used for decisions you make. It sounds like you are saying "people want you to graduate this year, but you have not decided if you really will or not. You will decide later." This is not the case. You "should" graduate and you "intend to do so".

I will be graduating from college this year. or I will graduate from college this year. If you say you are supposed to graduate from college, it sounds like there might be a problem and it might not happen. It sounds like you are worried about it, like: "I am supposed to graduate from college, but I did not pass one of my classes, and I must take the class over, or take the class again, since I "failed" the class."

This is the year of my university graduation. I am graduating from university this year. I shall graduate from my university this year. "Supposed to" is negativism and/or meaning that you are not sure if you'll graduate, or that you are not graduating at all. ( ex: you fail one year or you quited)