A combined stamping–bulging forming process was proposed to achieve high-precision forming of large-diameter, ultra-thin-walled, superalloy welded S-type corrugated diaphragms. The underlying principle is to enhance the diaphragm’s forming accuracy by increasing the plastic deformation region and reducing springback. Using the ABAQUS version 6.14 finite element analysis software, finite element models were constructed for the stamping, hydraulic bulging, and combined stamping–bulging forming processes of the welded S-type metal corrugated diaphragms. A comparative analysis was conducted on the forming processes of the welded S-type metal corrugated diaphragms under the three forming methods, focusing on equivalent stress, distribution of wall thickness, and forming accuracy. This analysis determined the optimal forming process and the corresponding process parameters for superalloy welded S-type metal corrugated diaphragms. The results show that under a constant drawing force, as the bulging pressure increases, the plastic deformation of the straight sections of the diaphragm becomes more pronounced, resulting in improved shape accuracy. The combined stamping–bulging forming process guarantees the highest degree of shape accuracy for the diaphragm. The optimal process parameters were identified as a 30 t force and a 5 MPa pressure, with a maximum shape error of 0.02 mm. Concerning a plate thickness of 0.3 mm, the maximum deviation rate was found to be 6.7%, which represents a 30% improvement over traditional stamping processes. The maximum wall thinning rate was found to be 3.3%, a 1% reduction compared to traditional stamping processes, confirming the process’s feasibility.