Hydrogels based on triblock copolymers of polyethylene glycol and partially methacrylated poly[N-(2-hydroxypropyl) methacrylamide mono/dilactate] make up an attractive class of biomaterials because of their biodegradability, cytocompatibility, and tunable thermoresponsive and mechanical properties. If these properties are fine-tuned, the hydrogels can be three-dimensionally bioprinted, to generate, for instance, constructs for cartilage repair. This study investigated whether hydrogels based on the polymer mentioned above with a 10% degree of methacrylation (M10P10) support cartilage formation by chondrocytes and whether the incorporation of methacrylated chondroitin sulfate (CSMA) or methacrylated hyaluronic acid (HAMA) can improve the mechanical properties, long-term stability, and printability. Chondrocyte-laden M10P10 hydrogels were cultured for 42 days to evaluate chondrogenesis. M10P10 hydrogels with or without polysaccharides were evaluated for their mechanical properties (before and after UV photo-cross-linking), degradation kinetics, and printability. Extensive cartilage matrix production occurred in M10P10 hydrogels, highlighting their potential for cartilage repair strategies. The incorporation of polysaccharides increased the storage modulus of polymer mixtures and decreased the degradation kinetics in cross-linked hydrogels. Addition of HAMA to M10P10 hydrogels improved printability and resulted in three-dimensional constructs with excellent cell viability. Hence, this novel combination of M10P10 with HAMA forms an interesting class of hydrogels for cartilage bioprinting.