Various 3D printing techniques currently use degradable polymers such as aliphatic polyesters to create well-defined scaffolds. Even though degradable polymers are influenced by the printing process, and this subsequently affects the mechanical properties and degradation profile, degradation of the polymer during the process is not often considered. Degradable scaffolds are today printed and cell-material interactions evaluated without considering the fact that the polymer change while printing the scaffold. Our methodology herein was to vary the printing parameters such as temperature, pressure, and speed to define the relationship between printability, polymer microstructure, composition, degradation profile during the process and rheological behavior. We used high molecular weight medical-grade (co)polymers—poly(L-lactide-co-ε-caprolactone) (PCLA), poly(L-lactide-co-glycolide) (PLGA), and poly(D, L-lactide-co-glycolide) (PDLGA)—with L-lactide content ranging from 25 to 100 mol percent, for printing in an extrusion-based printer (3D Bioplotter®). Optical microscopy confirmed that the polymers were printable at high resolution and good speed, until a certain degree of degradation. The results show also that printability can not be claimed just by optimizing printing parameters and highlight the importance of a careful analysis of how the polymer’s structure and properties vary during printing. The polymers thermally decomposed from the first processing minute and caused a decrease in the average block length of the lactide blocks in the copolymers and generated lower crystallinity. Poly(L-lactide) (PLLA) and PCLA are printable at a higher molecular weight, less degradation before printing was possible, compared to PLGA and PDLGA, a result explained by the higher complex viscosity and more elastic polymeric melt of the copolymer containing glycolide (GA) and lactide (LA). In more detail, copolymers comprising of LA and ε-caprolactone (CL) formed lower molecular weight compounds over the course of printing while the PLGA copolymer was more susceptible to intermolecular transesterification reactions, which do not affect the overall molecular weight but cause changes in the copolymer microstructure. This results in a longer printing time for PLGA than PLLA and PCLA.