This review covers the decomposition mechanisms of various printing ink binder resins, with a particular focus on their behavior under extrusion conditions in the mechanical recycling process of polyolefin (PO) based plastic packaging. Thermal degradation and hydrolysis of the nitrocellulose (NC) — the most used binder for flexographic surface printing on single-layer flexible plastic packaging, occur concurrently during the mechanical recycling process under 160–210 °C. For other printing ink binders, polyurethane (PU) noticeable degradation takes place between 200 and 300 °C, mostly above 250 °C. However, with the involvement of humidity, degradation by hydrolysis can start from 150 °C. A similar effect is also discovered with the cellulose acetate (CA) derivatives, which are thermally stable until 300 °C and can be hydrolyzed at 100 °C. The thermal stability of polyvinyl butyral (PVB) is not influenced by humidity, with thermal stability ranging from 170 to 260 °C, depending on different types. Ultraviolet (UV)-cured acrylics are thermally stable until 400 °C. The hydrolysis degradation can take place at room temperature. Moreover, this review covers the thermal stability of different colorants used for printing ink application and elaborates on several thermal-stable alternatives of some common colors. This study further reviews how the binder resin affects the quality of recyclates, revealing it to be not only induced by the degradation of the binder resin but also by the immiscibility between the plastic and binder resin. In advanced recycling processes, mainly selective dissolution-precipitation and pyrolysis, the presence of binder resin and its degradation products could still affect the quality of the product. This review accentuates the imperative need for in-depth research to unravel the impact of printing ink constituents on the quality of recycled products.