The capability and applicability of additive manufacturing have mesmerized the entire manufacturing world. One major technique of additive manufacturing is extrusion-based additive manufacturing (EAM), which has been recently employed for the rapid production of ceramic components, among other applications. This study focused on establishing the process-property relations for extrusion-based additively manufactured ceramics, namely Alumina (Al2O3) and Zirconia (ZrO2), and then optimization of the relations to get the desired mechanical properties for applicability. Extrusion-based additive manufacturing was used to obtain the ceramic sample parts from ceramic-binder mixtures and by subsequent post-processing. The process parameters chosen for the study were extrusion velocity and part orientation whereas the mechanical properties selected were hardness and flexural strength. Extrusion velocity was varied at three levels i.e. 7.5 mm/s, 12.5 mm/s and 17.5 mm/s. Two levels selected for part orientation were horizontal and vertical. The design of experiments technique was used to establish the process-property relations by highlighting the most significant process parameters affecting the selected mechanical properties. Optimization was achieved by highlighting those levels of significant process parameters that provided the desired values of mechanical properties. Part orientation came out to be a significant factor affecting both the hardness and flexural strength of the two ceramics whereas extrusion velocity was found to be insignificant for both mechanical properties. Among the two levels of part orientation, vertical orientation samples showed higher values of hardness while horizontal samples showed higher flexural strength thus, aiding in the optimization of the process-property relations.