This study conducted an in-depth examination of the delamination process of multi-layer packaging waste (MLPW) recycling, intending to find an effective solution for recycling MLPW. The recycling process for such materials can be challenging due to the complexity of separating the different layers and components. However, this study proposed using nitric acid to facilitate delamination and recover the polymers from multilayer food packaging—the research aimed to investigate the mechanical properties of the polymers obtained through this recycling method. Our study on polymer materials exposed to chemicals revealed differences in fracture and tensile strengths among three polymers, P1, P2, and P3. P1 showed fluctuating fracture strengths between 5.11 MPa and 3.55 MPa, while P2 maintained a consistent but lower value of around 0.09 MPa. P3 exhibited a wider range from 3.19 MPa to 1.79 MPa. Tensile strength analysis showed P1 averaging 4.99 MPa and P3 3.17 MPa, with P2’s data inconclusive due to its softness. Understanding the mechanical characteristics of recycled polymers is crucial to determine their potential use in different industries, including packaging, construction, or manufacturing, thereby promoting a more environmentally friendly approach to MLPW management.