The surface quality and production efficiency of continuous-casting steel slabs are predominantly determined by the performance of the mold. To address slab corner defects and enhance operational stability, this study systematically optimized two key components: the broad-face clamping mechanism and the narrow-face copper plate. A disk spring–hydraulic composite clamping mechanism was designed and subjected to mechanical analysis to ensure sufficient and reliable clamping force under high-load casting conditions. Meanwhile, based on the principle of solidification shrinkage, an external chamfer structure for the narrow-face copper plate was proposed to improve heat transfer uniformity at the slab corner. Engineering design calculations and practical application in an export-oriented wide-and-heavy slab continuous-casting project (specification: 250 mm × 2500 mm) demonstrated that the optimized clamping mechanism provides enhanced structural rigidity, while the new narrow-face copper plate effectively mitigates corner cracks and reduces wear. This integrated design approach significantly improves slab surface quality and extends component service life, yielding substantial economic benefits.