Most semi-circular bend (SCB) tests on concrete have been conducted with a pre-crack with a straight-through tip, thereby undermining the determination of the tensile fracture toughness (KIc). Therefore, the present study involved mixed-mode (tensile–shearing) fracture propagation in concrete semi-circular chevron-notched disks (i.e., with a sharp notch tip) using SCB tests and the FRANC2D numerical simulation software. The inclined notch angle (β) was varied from 0° to 70° while the other settings remained fixed, and the crack mouth opening displacement (CMOD) of the notch was measured constantly. The stress distribution was analyzed using finite-element simulations, and the experimental results showed that this testing method was robust. The maximum failure load and the fracture propagation angle increased with β, and wing fracture was observed. With FRANC2D simulating these SCB tests successfully, it was found that the tensile stress concentration around the notch tip moved toward the upper face of the notch, and the compressive stress concentration formed on the notch tip. The tensile mode was generated as the CMOD kept increasing for β = 0–30°, whereas the mixed mode became more evident as the CMOD kept decreasing for β = 45–70°. The fracture process zone was found for β = 0–30° but not for β = 45–70°. This mixed-mode fracture is predicted better by the criterion of extended maximum tangential strain than by other criteria, and there is a linear relationship between CMOD and KIc, as examined previously for pavement and concrete materials.