To overcome the inherent trade-off between high spectral resolution and low optical loss in on-chip speckle spectrometers, we propose a novel spectrometer architecture that cascades a Phase-Delayed Arrayed waveguide with a multimode waveguide (MMW). In this scheme, the Phase-Delayed Arrayed waveguide is utilized to introduce wavelength-dependent phase delays, which are subsequently transformed into transverse variations of the optical field at the input of the multimode waveguide. These variations can excite and reconfigure different internal modal distribution within the multimode waveguide, thereby enhancing the sensitivity of the output speckle patterns to wavelength changes. Simulation results convincingly demonstrate the superiority of this "phase-space-mode" cascaded enhancement mechanism: a device integrating a 50 GHz Phase-Delayed array with a 3mm×20μm MMW (1.44 mm2) achieves the spectral resolution of 0.72 pm at 1550 nm while maintaining a low optical loss of only 1.69 dB. Compared with existing counterparts, this design substantially enhances spectral resolution while effectively reducing device footprint and loss, offering a promising pathway for high-performance on-chip spectrometers.