Heterostructured materials consist of heterogeneous zones with dramatic variations in mechanical properties, and have attracted extensive attention due to their superior performance. Various heterostructured materials have been widely investigated in recent years. In the present study, a combination of two different types of heterogeneous structures, a surface bimodal structure and gradient structure, was designed using the traditional surface mechanical attrition treatment (SMAT) method in pure copper, and the mechanical properties and microstructural evolution of dual-heterostructure Cu were studied in depth. In total, 100 stainless steel balls with a diameter of 6 mm were utilized to impact the specimen surface at room temperature for a short period of time. In this work, the sample surface was divided into hard areas and soft areas, along with a roughly 90 μm gradient structure in the cross-sectional direction after 30 s of SMAT processing. After the partial SMAT processing, lasting 30 s, the strength increased to 158.0 MPa and a considerable ductility of 25.7% was sustained, which overcomes the strength–ductility trade-off. The loading–unloading–reloading (LUR) test was utilized to measure the HDI stress, and the result showed that the HDI stress of the partial SMAT sample was much higher than the annealed one, especially for the Cu-SMAT-30S specimen, the strength of which increased from 80.4 MPa to 153.8 MPa during the tensile test. An in situ digital image correlation (DIC) investigation demonstrated that the strain developed stably in the Cu-SMAT-10S specimen. Furthermore, electron backscatter diffraction (EBSD) was carried out to study the microstructural evolution after partial SMAT processing; the KAM value increased to 0.34 for the Cu-SMAT-10S specimen. This research provides insights for the effective combination of superior strength and good ductility in dual-heterostructure materials.