Basically, we tend to celebrate events where something is happening. (Or a specific event has just happened.) The Talmud described celebrations when semicha was conferred on someone, which has loosely translated into contemporary semicha-granting parties. (Though our semicha today is much more like a graduation.)
So I'm not aware of a graduation tradition per se. We celebrate an accomplishment like completing a book; but what does "I'm done with school" mean for a faith that stresses ongoing study for life?
On the other hand, Rabbi Mordechai Willig has fascinatingly suggested that a father's prayer at his son's bar mitzvah of "thank you G-d for exempting me" means that a father has now fulfilled his bare-bones obligations of educating his son, if the son is now able to read the Torah on his own.
The Sforno observes that the Torah uses passive language for people who are merely acted-upon -- the entire code describing the metzora is all "his place to sit is out here. He shall be brought... this shall be done to him." The exception is the Nazir who has finished the terms of his oath: "he shall bring himself to the Temple." While his completion of the term is passive, it will surely lead to active contemplation of his life moving forward -- which is a great message for graduates.
Lastly, a teacher of mine told me of his father's high school graduation from Mesivta Tifereth Jerusalem in New York. He said the yearbook featured a letter from Rabbi Moshe Feinstein to the effect of: "I hear there's this thing called a graduation going on, I asked what it was all about ... it was explained to me that they now have a break from their formal studies and can spend more time learning Torah -- so I join in the rejoicing!" (I haven't seen the letter, that's how I heard the gist of it described.)