Clay-based additive manufacturing is gaining attention as a route for producing construction materials with reduced environmental impact, particularly when combined with locally sourced waste-derived additives. However, incorporating bio-based residues into printable clay systems requires an understanding of their roles within the matrix, as not all additives serve as mechanical reinforcements. This study examines extrusion-based additive manufacturing of clay composite bricks containing eggshell powder, spent coffee grounds, and hay fibers. A commercial hydrated clay was used as the reference matrix. Eggshell powder was incorporated as a biogenic calcium carbonate filler, spent coffee grounds as a sacrificial organic pore-forming agent, and hay fibers as short natural fibers intended to enhance green-state stability and contribute to post-firing porosity. Prismatic bricks with nominal dimensions of 160 × 40 × 40 mm were fabricated. The experimental matrix comprised neat clay, clay with 7–8 wt% eggshell powder, clay with 2.5–5 wt% spent coffee grounds, and clay with 7 wt% hay fibers. Preliminary results indicate that additive morphology and water content strongly influenced extrusion stability, shape retention, drying behavior, and post-processing integrity. The 7 wt% eggshell formulation showed good compatibility with the clay matrix, supporting stable deposition at 0.4 MPa, consistent brick formation, and accelerated drying. In contrast, mixtures containing spent coffee grounds were more sensitive to water content. The organic phase was removed during kiln firing, which contributed to porosity development but required stricter moisture control to mitigate drying and firing defects. Hay fibers provided a fibrous phase during shaping and drying and acted as burnout agents after firing. Material characterization included compression and buckling tests, SEM analysis of pore morphology and fracture surfaces, and XRD analysis of phase evolution after firing. These findings provide an experimental basis for developing waste-derived porous clay composites through extrusion-based additive manufacturing for sustainable, non-structural construction applications.