Combining recycling of paper wastes (WPs) with extrusion‐based additive manufacturing represents a sustainable route to cellular cellulose composites tailored for lightweight construction. Particularly, shear mixing of shredded WPs with an aqueous solution of a polymer binder like polyvinyl alcohol (PVA) yields aqueous pastes suitable for 3D printing. As a shear thinning additive, both WP and microfibrillated cellulose account for enhanced shear thinning and dimensional stability. Opposite to the formation of dense WP/PVA composites by melt extrusion, 3D printing of aqueous pastes produces cellular cellulose/PVA composites exhibiting hierarchical pore architectures. In spite of low densities around 0.8 g cm−3, high Young’s modulus (2.0 GPa) and tensile strength (53 MPa) are achieved. Mechanical stability, water resistance, and even flame retardancy simultaneously improve by crosslinking with glyoxal and especially by mineralization. Multimaterial 3D printing combines the 3D dispensing of cellulose/PVA pastes with the simultaneous, staged, or subsequent spraying of aqueous water glass to enable mineralization of composite surface, bulk, and interlayers. Furthermore, the glyoxal‐mediated crosslinking affords thermo‐ and moisture‐responsive cellulose/PVA composites with programmable shape change induced either by heating at 100 °C or by exposure to moisture at 37 °C.