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We observe that many state-of-the-art open-source web agents rely on long tool-call trajectories with cyclic reasoning loops and exploration of unproductive branches. To address this, we propose WebClipper, a framework that compresses web agent trajectories via graph-based pruning. Concretely, we model the agent's search process as a state graph and cast trajectory optimization as a minimum-necessary Directed Acyclic Graph (DAG) mining problem, yielding pruned trajectories that preserve essential reasoning while eliminating redundant steps. Continued training on these refined trajectories enables the agent to evolve toward more efficient search patterns and reduces tool-call rounds by about 20% while improving accuracy. 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