In this work, the authors investigated the impact of extrusion-based printing process on the structural characteristics of bio-based resins through rheological measurements. Two commercially available filaments made from unfilled and wood-filled polylactide (PLA) polymers were considered. Three-dimensional specimens were prepared by printing these filaments under various operating conditions, i.e., changing the extruder temperature and printing rate, and examined using time sweep tests. Specific cycle rheological testing was conducted on pelletized filaments to simulate temperature changes in the printing process. The rheological characteristics of unprocessed materials, in terms of storage (G') and loss (G″) moduli, were found to be slightly affected by temperature changes. For a pure polymer, the G' slope at a low frequency decreased over time, showing that the polymer chains evolved from a higher to a lower molecular weight. For wood-filled materials, the G' slope rose over the testing time, emphasizing the formation of a percolated network of structured filler within the matrix. On the other side, the rheological parameters of both materials were strongly impacted by the printing extrusion and the related conditions. At lower nozzle temperatures (200 °C), by decreasing the printing speed, the G' and G″ curves became increasingly different with respect to unprocessed resin; whereas at higher nozzle temperatures (220 °C), the influence of the printing speed was insignificant, and all curves (albeit distant from those of unprocessed matrix) mainly overlapped. Considerations on degradation kinetics of both materials during the printing process were also provided by fitting experimental data of complex viscosity with linear correlation over time.