Fused Filament Fabrication (FFF) is a polymer-based Additive Manufacturing (AM) technology that produces intricate layered components. The characterization of their orthotropic properties and their failure analysis is a challenging task. In this study, a Mechanism-Based (MB) damage material model is developed to analyse the failure mechanisms of FFF parts. A multiscale orthotropic material model previously tested and validated in [1, 2] is used to characterize the mechanical behaviour of FFF components. This work proposes a MB damage criterion, which takes into account the different failure modes inherent to each specific printing pattern. The criterion is then compared to the commonly used Tsai-Wu (TW) criterion, designed for orthotropic materials with different strengths in tension and compression. Additionally, a MB cracking model that incorporates the orthotropic brittleness specific to FFF components is developed. Numerical predictions of two experimental tests demonstrate the similarities and differences between the MB and TW damage criteria. The results show that the MB damage criterion accurately agrees with the experimental outcomes, whereas the TW criterion fails to describe correctly the failure modes in complex 3D stress states.