Random body movements during frequency modulated continuous wave (FMCW) radar-based vital sign monitoring can induce abrupt phase variations, range-bin shifts, and spectral peak deviations, thereby degrading the estimation accuracy of respiratory rate (RR) and heart rate (HR). To address this issue, a vital sign detection algorithm for non-stationary subjects is proposed. First, the phase of the radar intermediate-frequency signal is used to construct a motion trend function based on the second-order phase difference, enabling the characterization of abrupt phase changes induced by random body movements. A dynamic threshold is then applied to identify motiondistorted segments. These segments are locally reconstructed using a seasonal autoregressive integrated moving average model (SARIMA), whereas segments without significant motion interference are preserved to avoid unnecessary global modeling. Respiratory rate and heart rate are subsequently estimated through signal separation and spectral analysis. Experimental results show that, when the dynamic threshold adjustment coefficient μ is set to 0.20, the heart rate estimation accuracy reaches 96.10%, with an RMSEHR of 1.653 3. Across different SARIMA parameter combinations, the recovered respiratory rate and heart rate remain stable; however, the running time of higher-order model increases from 57.106 1 s to 335.748 4 s. Further experiments involving four subjects demonstrate that the proposed algorithm achieves a respiratory rate detection accuracy of 93.33% and a heart rate detection accuracy of 96.90%, with corresponding RMSERR and RMSEHR values of 3.43 and 11.01, respectively. These results indicate that, under the random-body-motion conditions considered in this study, the proposed method can reduce the influence of motion interference and improve the stability of respiratory-rate and heart-rate estimation.