Policy documents shape governance outcomes, but their reasoning is often implicit, with tensions between participatory commitments and managerial control rarely stated directly. Existing computational approaches to policy discourse cannot express the frame-mediated relations that drive these tensions, where one argument narrows or instrumentalizes another, and end-to-end summarization by large language models offers little structure that domain experts can inspect or contest. To address this, we present **D-APA** (Discourse-aware Argumentative Policy Analysis), a hybrid LLM–symbolic pipeline that operationalizes critical discourse policy analysis as a quantitative argumentation graph. Given a policy text, an LLM first extracts its arguments, where each argument is classified into a *deliberative* or *managerial* frame and scanned for discourse features such as agency type and verb class. Deterministic rules over these features then connect the arguments through four frame-mediated relation subtypes, namely *agency reduction*, *agenda shift*, *instrumental support*, and *normative support*. Finally, argumentation semantics propagates linguistically grounded base scores through the resulting graph, yielding a final strength for every argument. We release a novel dataset of 100 sub-documents of disaster-risk-reduction policy from the USA, UK, Canada, and Australia, and show that our pipeline produces argument graphs that are accurate, interpretable, and consistent across jurisdictions.