To determine the optimal construction method for highway tunnels in strongly weathered rock strata, this study conducts numerical simulations based on actual geological conditions of strongly weathered rock. The influence of three construction methods—the two-bench reserved core soil annular excavation method, the CRD (cross diaphragm) method, and the double-side drift method—on the stability of tunnel surrounding rock is systematically analyzed from three perspectives: surrounding rock deformation and displacement, plastic zone distribution characteristics, and technical-economic indicators. The results indicate that the CRD method achieves the most favorable deformation control, effectively mitigating the risk of crown settlement and maintaining tunnel structural stability. This method also yields the smallest extent of plastic zone distribution and the best overall surrounding rock stability. In terms of economic and construction management considerations, although the CRD method entails higher initial investment and more complex construction organization, it reduces long-term maintenance costs and the risk of construction delays, with moderate material consumption and construction speed, thereby offering significant technical and economic benefits. The findings of this study provide a theoretical basis and engineering reference for the selection of construction methods for highway tunnels in highly weathered rock strata.