In the present study, we develop a high-fidelity computational framework tailored for compressible wall-bounded turbulent flows, with its core implementation built upon the cut-cell method. Specifically, (i) the framework enables low-dissipation and accurate simulation of compressible turbulent flows using the hybrid TENO-KEEP scheme, which serves as an implicit large-eddy simulation (ILES) model for turbulence closure; (ii) the cut-cell method serves as a sharp interface approach for complex geometries while minimizing numerical dissipation near solid boundaries; (iii) a novel wall model, based on recently proposed inverse velocity and temperature transformations, is integrated into the cut-cell framework to reliably predict compressible wall-bounded turbulence; (iv) lastly, the highly efficient parallelization is achieved on a block-structured Cartesian grid combined with adaptive mesh refinement (AMR). Comprehensive validations include numerical accuracy tests, moving-geometry cases, and simulations spanning flow regimes from low Mach numbers (Ma at 0.2) to hypersonic speeds (Ma up to 8). Challenging real-world engineering simulations further verify the framework's accuracy, and scalability tests confirm its excellent parallel efficiency.