The addition of biocarriers can improve biological processes in bioreactors, since their surface allows for the immobilization, attachment, protection, and growth of microorganisms. In addition, the development of a biofilm layer allows for the colonization of microorganisms in the biocarriers. The structure, composition, and roughness of the biocarriers’ surface are crucial factors that affect the development of the biofilm. In the current work, the aluminosilicate zeolites 13X and ZSM-5 were examined as the main building components of the biocarrier scaffolds, using bentonite, montmorillonite, and halloysite nanotubes as inorganic binders in various combinations. We utilized 3D printing to form pastes into monoliths that underwent heat treatment. The 3D-printed biocarriers were subjected to a mechanical analysis, including density, compression, and nanoindentation tests. Furthermore, the 3D-printed biocarriers were morphologically and structurally characterized using nitrogen adsorption at 77 K (LN2), scanning electron microscopy (SEM), and X-ray diffraction (XRD). The stress–strain response of the materials was obtained through nanoindentation tests combined with the finite element analysis (FEA). These tests were also utilized to simulate the lattice geometries under compression loading conditions to investigate their deformation and stress distribution in relation to experimental compression testing. The results indicated that the 3D-printed biocarrier of 13X/halloysite nanotubes was endowed with a high specific surface area of 711 m2/g and extended mesoporous structure. Due to these assets, its bulk density of 1.67 g/cm3was one of the lowest observed amongst the biocarriers derived from the various combinations of materials. The biocarriers based on the 13X zeolite exhibited the highest mechanical stability and appropriate morphological features. The 13X/halloysite nanotubes scaffold exhibited a hardness value of 45.64 MPa, which is moderate compared to the rest, while it presented the highest value of modulus of elasticity. In conclusion, aluminosilicate zeolites and their combinations with clays and inorganic nanotubes provide 3D-printed biocarriers with various textural and structural properties, which can be utilized to improve biological processes, while the most favorable characteristics are observed when utilizing the combination of 13X/halloysite nanotubes.