Additive manufacturing (AM) of continuous yarn-reinforced biobased composites presents multi-functional properties and low environmental impact of this technology. Few studies focused on the mechanical damage mechanisms of continuous biobased composites obtained by AM processes, while it is a topic of high interest for the mastery of mechanical behaviors and optimization of the materials for high requirement applications. This study aims to assess the damage and fracture modes of continuous flax yarn-reinforced PLA manufactured by AM, with different yarn orientations. The additively manufactured biobased composites were characterized by tensile test, 3D microscopy and micro-tomography to link the process-structure-properties relationships regarding the damage and fracture modes. The results showed that the 0° manufactured composite had a significant enhancement of tensile properties compared to other configurations. The damage mechanism presented fiber rupture with polymer transverse cracks at 0°, while the 45° and 90°-oriented composites showed premature fiber/matrix interface debonding. This study aims to find the relationship between damage mechanisms, deposition strategy, and anisotropy of the additively manufactured long vegetal fibers-reinforced biobased composite materials. The results bring a new understanding of the anisotropy and defects in printed composite materials regarding their mechanical behaviors during damage.