Three-dimensional printing, especially the technology of fused deposition modelling (FDM), is more and more often used for the production of different objects, especially those that are produced only in small numbers or that have complicated shapes that cannot be produced in a different way. The increase in 3D-printed objects, on the other hand, leads to an increase in polymeric waste that has to be taken into account. One way to reduce this problem is using biodegradable thermoplastic polymers instead of petroleum-based plastics, which are responsible for “white pollution”. Amongst the biodegradable, biobased polymers used for 3D printing, poly(lactic acid) (PLA) is most commonly used, while polyhydroxyalkanoates (PHA) and a few other materials are also under investigation for 3D printing. PLA, however, has a much slower degradation rate under environmental conditions than other biopolymers and actually needs commercial composting. This is why a study was performed investigating the printability of different biobased FDM filaments with better biodegradability. In addition, the mechanical properties and surface morphology of the 3D-printed objects were compared with those of PLA and PETG. Due to the potential use of such filaments in tissue engineering and other biomedical applications, the chemical stability and the possibility of autoclaving the biobased materials were also successfully tested. The results of this study show the potential of new biobased FDM filaments for biomedical and biotechnological applications.