In this study, we investigated the performance improvement caused by the addition of copper (Cu) nanoparticles to high-density polyethylene (HDPE) matrix material. Composite materials, with filler percentages of 0.0, 2.0, 4.0, 6.0, 8.0, and 10.0 wt% were synthesized through the material extrusion (MEX) 3D printing technique. The synthesized nanocomposite filaments were utilized for the manufacturing of specimens suitable for the experimental procedure that followed. Hence, we were able to systematically investigate their tensile, flexural, impact, and microhardness properties through various mechanical tests that were conducted according to the corresponding standards. Broadband Dielectric Spectroscopy was used to investigate the electrical/dielectric properties of the composites. Moreover, by employing means of Raman spectroscopy and thermogravimetric analysis (TGA) we were also able to further investigate their vibrational, structural, and thermal properties. Concomitantly, means of scanning electron microscopy (SEM), as well as atomic force microscopy (AFM), were used for the examination of the morphological and structural characteristics of the synthesized specimens, while energy-dispersive X-ray spectroscopy (EDS) was also performed in order to receive a more detailed picture on the structural characteristics of the various synthesized composites. The corresponding nanomaterials were also assessed for their antibacterial properties regarding Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli) with the assistance of a method named screening agar well diffusion. The results showed that the mechanical properties of HDPE benefited from the utilization of Cu as a filler, as they showed a notable improvement. The specimen of HDPE/Cu 4.0 wt% was the one that presented the highest levels of reinforcement in four out of the seven tested mechanical properties (for example, it exhibited a 36.7% improvement in the flexural strength, compared to the pure matrix). At the same time, the nanocomposites were efficient against the S. aureus bacterium and less efficient against the E. coli bacterium. The use of such multi-functional, robust nanocomposites in MEX 3D printing is positively impacting applications in various fields, most notably in the defense and security sectors. The latter becomes increasingly important if one takes into account that most firearms encompass various polymeric parts that require robustness and improved mechanical properties, while at the same time keeping the risk of spreading various infectious microorganisms at a bare minimum.