Frequency-sweeping interferometry (FSI) is an advanced coherent measurement technique capable of simultaneous high-precision measurement of dynamic target absolute distance and velocity. This study reveals that the dynamic target modulates the beat signal in FSI, causing the phase jump phenomenon in the beat signal and subsequent measurement failures. We theoretically derive and experimentally validate the conditions for phase jumps. Additionally, we propose using time-frequency analysis methods to detect phase jump instants and reconstruct the instantaneous frequency trajectory of the beat signal modulated by phase jumps. Experimental results show that even with phase jumps, we achieved a dynamic velocity measurement of −135.40 mm/s on a 0.5 m baseline, surpassing the theoretical limit of −4.40 mm/s under this baseline, while maintaining effective measurement capability on an extended 10 m baseline. The discovery and resolution of phase jumps are expected to overcome velocity limitation in FSI, significantly expanding its velocity measurement range.