Trailing-edge noise is the dominant contributor to the noise generated by aircraft and wind turbines. Serrations on the trailing edge play a crucial role in suppressing the aerodynamic noise of an airfoil, and bionic airfoil sections are confirmed to be rewarding to sound suppression. However, how these characteristics affect the noise emission is still unknown. In this study, the bio-inspired oblique trailing-edge serrations are embedded within the trailing edge of the airfoil with unique cross section of the owl wing, which differs from the previous design. The noise reduction mechanism of coupled airfoils with innovative asymmetric and conventional trailing-edge serrations are explored at a low Mach number. Numerical results show that the largest lift-to-drag ratio with 17.69 and the smallest sound pressure level with 15.72 dB for the airfoil with bio-inspired oblique serrations are obtained among the investigated airfoils. An additional noise reduction of 3.68 dB can be achieved by using innovative asymmetric serrations. Moreover, the widespread large-scale disordered vorticities triggered by smooth airfoil on the pressure side are detached into the smaller-scale vortices triggered by coupled airfoil. The spanwise correlation reflecting the noise emission is significantly decreased. Distinguishingly, more turbulent kinetic energy and pressure fluctuations are emitted in the longitudinal direction on account of the intense collision of the airflow and the gap flow generated by conventional serrations. It is expected that this in-depth study of sound suppression will serve as an essential guide for airfoil design and noise control for micro-aircraft and fluid machinery coping with disturbing areas.