This experimental work aims at evaluating the mechanical and failure behavior of adhesive-bonded single-lap joints made of a thermoplastic composite 3D-printed via Fused Filament Fabrication technology. Carbon fiber was selected as the reinforcement and used in the form of both short and continuous fibers embedded in the Nylon-6 matrix, forming the composite’s hybrid structure. An approach based on progressive improvement of surface treatment effectiveness (solvent degreasing, abrasion, and low-pressure plasma) has been adopted to verify how the additively-manufactured composite responds to bonding when increased interfacial adhesion is attained by preparing the outer printed layer. Roughness measurements, wettability evaluations, and XPS analyses have been carried out to assess any modifications of morphology and functionalization exhibited by the different surfaces after treatment. The experimental findings demonstrate that the intrinsic non-homogeneity of 3D-printed composites is emphasized when low-pressure plasma is used, as it generates interfacial bonds between adhesive and adherend that are more effective than the interlaminar ones within the substrate. In this condition, the ultimate resistance of the joint corresponds to that of the base material. In particular, fracture-mechanism analysis allowed precise identification of the crack path, highlighting defects and current limitations of the additively-manufactured system and suggesting pivotal aspects to develop in future work to improve joint performance.