Cellulose is an abundant and sustainable material that is receiving more and more attention in different industries. In the context of additive manufacturing, it would be even more valuable. However, there are some challenges to overcome in processing cellulose-based materials. Therefore, this study used a new thermoplastic cellulose-based granulate to show its potential in filament extrusion and the fused filament fabrication printing process. Furthermore, the mechanical properties were investigated. It was shown that filaments with a suitable and uniform diameter could be produced. A parameter study for printing revealed that adhesion of the material on the bed and between layers was an issue but could be overcome with a suitable set of parameters. Tensile bars with different orientations of 0°, +/−45°, and 90° were printed and compared with injection-molded samples. It could be shown that different mechanisms (single strand breakage, shear failure) caused fracture for different printing orientations. In comparison with injection-molding, the printed parts showed lower mechanical properties (moduli of 74–95%, a tensile strength of 47–69%, and an elongation at break of 29–60%), but an improvement could be seen compared with earlier reported direct granule printing. The study showed that FFF is a suitable process for the new cellulose-based material to fabricate samples with good mechanical properties.