The increasing complexity of modern AI systems exposes a significant assurance gap: safety evidence from practices like red-teaming and robustness testing remains fragmented, lacking a formal mechanism for composition and propagation throughout the development lifecycle. This prevents the construction of rigorous, dynamic safety cases essential for trustworthy AI. We introduce the Composable Assurance Framework (CAF), a novel engineering methodology that integrates safety assurance directly into MLOps workflows. At its core is the Formal Safety Assertion (FSA), a standardized, machine-readable structure that verifiably links safety properties—such as robustness scores or the absence of deceptive circuits—to specific AI artifacts. We then define a Composition Calculus, a set of formal rules governing how FSAs are propagated and aggregated as components are combined into a system. This approach transforms the development pipeline into an automated evidence-gathering engine, whose output is a dynamic Directed Acyclic Graph (DAG) of assertions that constitutes a living safety case. Through a prototype and a Retrieval-Augmented Generation (RAG) case study, we demonstrate how CAF automatically enforces a predefined safety policy, blocking non-compliant deployments.