Recently, people have suffered and become increasingly aware of the unreliability gap in LLMs for open and knowledge-intensive tasks, and thus turn to search-augmented LLMs to mitigate this issue. However, when the search engine is triggered for harmful tasks, the outcome is no longer under the LLM's control. Once the returned content directly contains targeted, ready-to-use harmful takeaways, the LLM's safeguards cannot withdraw that exposure. Motivated by this dilemma, we identify web search as a critical attack surface and propose \textbf{\textit{SearchAttack}} for red-teaming. SearchAttack outsources the harmful semantics to web search, retaining only the query's skeleton and fragmented clues, and further steers LLMs to reconstruct the retrieved content via structural rubrics to achieve malicious goals. Extensive experiments are conducted to red-team the search-augmented LLMs for responsible vulnerability assessment. Empirically, SearchAttack demonstrates strong effectiveness in attacking these systems.