Airborne terahertz synthetic aperture radar (THz SAR) represents a significant advancement in instrumentation for ground moving target imaging (GMTIm), enabling high resolution measurements at a high frame rate. However, the short wavelength of THz SAR results in high Doppler sensitivity. This means that platform vibrations become a critical source of measurement error, which severely degrades the accuracy of Doppler parameter estimation and the refocusing performance when conventional methods are used. Firstly, a phase gradient vibration separation (PGVS) algorithm is developed to isolate and compensate for vibration-induced phase distortions while preserving the intrinsic target motion signatures essential for precise measurement. Subsequently, a computationally efficient downsampling polynomial-phase decoupling (DPD) algorithm accurately estimates Doppler parameters, overcoming the limitations of high pulse repetition frequency (PRF) sampling. The proposed method is validated using measured data from a SAR system with a center frequency of 0.22 THz. The results demonstrate a significantly improved refocusing quality, as evidenced by reduced image entropy and enhanced contrast. This work provides a robust solution for high precision GMTIm using emerging THz SAR systems.