In the biomedical field, extrusion-based 3D bioprinting has emerged as a promising technique to fabricate tissue replacements. However, a main challenge is to find suitable bioinks and reproducible procedures that ensure good printability and generate final printed constructs with high shape fidelity, similarity to the designed model, and controllable mechanical properties. In this study, our main goal is to 3D print multilayered structures from alginate-gelatin (AG) hydrogels and to quantify their complex mechanical properties with particular focus on the effects of the extrusion process and geometrical parameters, i.e. different mesostructures and macroporosities. We first introduce a procedure including a pre-cooling step and optimized printing parameters to control and improve the printability of AG hydrogels based on rheological tests and printability studies. Through this procedure, we significantly improve the printability and flow stability of AG hydrogels and successfully fabricate well-defined constructs similar to our design models. Our subsequent complex mechanical analyses highlight that the extrusion process and the mesostructure, characterized by pore size, layer height and filament diameter, significantly change the complex mechanical response of printed constructs. The presented approach and the corresponding results have important implications for future 3D bioprinting applications when aiming to produce replacements with good structural integrity and defined mechanical properties similar to the native tissue, especially in soft tissue engineering. The approach is also applicable to the printing of gelatin-based hydrogels with different accompanying materials, concentrations, or cells.