Well, this is one of the much debated questions since the first show of this play. Though Chekhov himself claimed this play as a farce, however many critics claim that tragic elements in this play overshadow its comical elements. Although this play does not fit into a typical definition of the tragedy, but it contains some definite tragic elements.
In contrast, yes it undoubtedly contains many farcical elements. For instance, the characters like Leonid Gayev constantly refer to his imaginary billiard shots, then Simon Yepikhodov and his love triangle, bring comedy in this play.
Yet interestingly, despite having comic elements, it is equally possible to call it both comic and tragic play due to the situations of its characters. Thus, it seems Chekhov has deliberately robbed readers of their ability to classify this literary piece into a separate category.