Acoustic metasurface, currently as a hot research topic, is used for wavefield manipulation. Its structure is typically designed according to generalized Snell's law by starting with heuristic or empirical configurations and adjusting geometric parameters to achieve better performance. However, this heuristic design approach cannot reach the performance limit due to diffraction effects at low frequencies. We therefore turn to topology optimization methods to push the limits of the metasurface. Although topology optimization has been widely applied to mechanical design, its application in acoustic field manipulation is still in the early stages. In this work, we present a novel optimization framework by using a density-based approach for designing acoustic metasurfaces to achieve two types of reflected wave propagation: (i) uniform diffusion and (ii) anomalous deflection. Unlike a local design strategy, this approach is considered global. It simultaneously expands the design parameter space of the metasurface and overcomes the theoretical limitations of thin-layer structures in acoustic wave manipulation. Simulation results demonstrate that the designed metasurface can achieve excellent uniform diffuse reflection (normalized diffusion coefficient greater than 0.9) at low frequencies (300 to 1000 Hz) and also large-angle deflection (reflection angle up to 75°). Overall, the incorporation of topology optimization methods grants more freedom to acoustic metasurface design, provides a more flexible approach to acoustic wave manipulation, and unlocks additional possibilities for beamforming techniques.