Winning competitive debates requires sophisticated reasoning and argument skills. There are unique challenges in the competitive debate: (1) The time constraints force debaters to make strategic choices about which points to pursue rather than covering all possible arguments; (2) The persuasiveness of the debate relies on the back-and-forth interaction between arguments, which a single final game status cannot evaluate. To address these challenges, we propose TreeDebater, a novel debate framework that excels in competitive debate. We introduce two tree structures: the Rehearsal Tree and Debate Flow Tree. The Rehearsal Tree anticipates the attack and defenses to evaluate the strength of the claim, while the Debate Flow Tree tracks the debate status to identify the active actions. TreeDebater allocates its time budget among candidate actions and uses the speech time controller and feedback from the simulated audience to revise its statement. The human evaluation on both the stage-level and the debate-level comparison shows that our TreeDebater outperforms the state-of-the-art multi-agent debate system, with a +15.6% improvement in stage-level persuasiveness with DeepSeek and +10% debate-level opinion shift win. Further investigation shows that TreeDebater shows better strategies in limiting time to important debate actions, aligning with the strategies of human debate experts.