The effect of screw speed and oyster mushroom addition on the texture characteristics (hardness, gumminess, and chewiness) and specific mechanical energy (SME) was determined via factorial experiment design. Individually increasing screw speeds had little effect compared to the effects of oyster mushroom addition. However, the combined effects of screw speed and oyster mushroom addition significantly reduced (p ≤ 0.05) all the texture characteristics. The hardness (3521.35 g) and gumminess (2717.85) of the meat analog extruded at the maximum screw speed of 160 rpm and 15% oyster mushroom addition are close to the chicken breast’s characteristics, respectively. The oyster mushroom–soy protein extrudates are chewier than the non-hydrated texturized vegetable protein (TVP) and chicken meats. The SME values of the single-screw extrusion were linearly affected by the increasing screw speed, which also lies in the range < 200 kJ/kg for producing meat analog with acceptable characteristics. Applying the superposition technique successfully shifted the individual curves of the SME into a smooth master curve vertically, allowing an interpolating in the prediction of SME value at a given screw speed value.