Don Quixote can certainly not be classified as a pure tragedy or a pure comedy. The protagonist, Don Quixote, is actually an anti-hero, or perhaps a pseudo-hero, which adds a comic element to everything he does, no matter how serious or well intended. He has tragically gone rather crazy, as well, adding another dimension of comedy. As he prepares to venture forth, we laugh at his armor, his buckler, his visor, and his horse--but we admire his determination and his heart and even his mission.
The tragic elements are certainly present, as well. We do understand what has happened to him, and we sympathize with the events which transpire. One definition of tragedy says someone from a high place must fall; Don Quixote is never really in a high place, though he does fall hard--over and over. He is mistreated and maligned by myriad people and groups, which is certainly tragic, if not a tragedy.
Because we understand his pure heart, his story is a tragedy; however, it would be impossible not to be at least amused by the antics and exploits of the irrepressible Don Quixote.