Identifying vital-related signals from human targets in a single synthetic aperture radar (SAR) image processing is important but challenging for localization and rescue applications. Recently, hybrid-mode SAR was reported for human identification and localization by alternating a radar in both the interferometry and frequency-modulated continuous-wave (FMCW) modes. However, it increased system complexity and required doubling the scanning efforts. In this paper, a novel phase-demodulation based vital-SAR-imaging method with a portable radar in pure FMCW mode is proposed. The solution can identify human targets from the SAR image by extracting high-resolution breathing signals on a moving platform. Experiments have been con-ducted to demonstrate the accuracy and robustness of the pro-posed method.