This paper explores the optimization of the interaction between the rotor and axial slot casing treatment (ASCT) to enhance both efficiency and stability margins. Previous studies primarily focused on rotor tip optimization, often compromising flow in non-tip regions and reducing overall rotor performance. To address these limitations, this study introduces a new optimization framework integrating full-span 3D blade design with a semicircular axial slot, utilizing both sequential and concurrent optimization strategies. The sequential approach first optimizes blade geometries, followed by ASCT adjustments, while the concurrent approach treats the blade and ASCT as a unified aerodynamic system. Compared to prior studies focusing exclusively on tip-only 3D shape optimization, results indicate that sequential coupled optimization improves the stall margin by 13.32% and efficiency by 0.05%, whereas the concurrent strategy further enhances performance, shaping the blades into an inverse S form, reducing efficiency losses from 0.12% to 0.02%, and increasing the stall margin increment from 14.88% to 21.83%. These findings demonstrate the significant performance gains achievable through coordinated rotor and ASCT design.