Stimuli-responsive biomaterials have progressively developed over the last decade in three-dimensional (3D) bioprinting, enabling dynamic regulation of bioink rheological and processing properties, printing fidelity, and the functional maturation of printed constructs. However, the rapid expansion of responsive materials and bioprinting technologies has led to fragmented and non-standardized definitions of biomaterials and bioinks, resulting in inconsistent classification approaches and complicating the analysis, comparison, and design of emerging systems, which highlights the lack of a unified framework for biomaterial selection for bioprinting. This article introduces the Bioprinting Biomaterials Classification (BBC) as a conceptual framework that provides a structured and design-oriented basis for biomaterial selection for bioprinting by linking stimulus-responsive behavior with stage-specific functional requirements across the bioprinting process. The BBC framework operates based on the classification of biomaterials according to two complementary dimensions, namely stimulus category (physical, chemical, and biological stimuli) and functional roles across the bioprinting lifecycle (bioink preparation, printing process, post-printing maturation, and in vivo function). This two-level biofunctional classification connects material responsiveness with biofabrication processes and enables a systematic interpretation of how responsive biomaterials can be selected and applied according to their stage-specific functional roles. It provides a systematic framework for positioning responsive biomaterials within the biofabrication context and supports a more structured and application-driven approach to biomaterial selection and design in bioprinting systems. By addressing the current lack of structured strategies for biomaterial selection for bioprinting, the BBC framework offers a foundational step toward a more rational and consistent design of responsive biomaterials in advanced biofabrication systems.