Query-focused table summarization requires complex reasoning, often approached through step-by-step natural language (NL) plans. However, NL plans are inherently ambiguous and lack structure, limiting their conversion into executable programs like SQL and hindering scalability, especially for multi-table tasks. To address this, we propose a paradigm shift to structured representations. We introduce a new structured plan, TaSoF, inspired by formalism in traditional multi-agent systems, and a framework, SPaGe, that formalizes the reasoning process in three phases: 1) Structured Planning to generate TaSoF from a query, 2) Graph-based Execution to convert plan steps into SQL and model dependencies via a directed cyclic graph for parallel execution, and 3) Summary Generation to produce query-focused summaries. Our method explicitly captures complex dependencies and improves reliability. Experiments on three public benchmarks show that SPaGe consistently outperforms prior models in both single- and multi-table settings, demonstrating the advantages of structured representations for robust and scalable summarization.