It is often referred to as a comedy, no doubt due to the subtitle and Chekhov's insistence on calling it a farce, but to me the tragic elements overwhelm the comic. This family, though terribly flawed, falls victim to its illusions. Although the cherry orchard in prior years was made possible by slave labor, it still seems unfortunate that it must be cut down, and tragic that the family members can't get out of fantasyland long enough to make decisions that might help them to save themselves.
It is sad and ironic that in trying to cling to the past, represented by the cherry orchard, they lose both the estate and the orchard itself, which is cut down anyway. They lose their status, they lose their home, and they go out into the world ill-equipped to adapt to new realities. If this is comedy, it is dark comedy; if it is farce, it is tragic farce.