In the context of multi-object tracking using video synthetic aperture radar (Video SAR), Doppler shifts induced by target motion result in artifacts that are easily mistaken for shadows caused by static occlusions. Moreover, appearance changes of the target caused by Doppler mismatch may lead to association failures and disrupt trajectory continuity. A major limitation in this field is the lack of public benchmark datasets for standardized algorithm evaluation. To address the above challenges, we collected and annotated 45 video SAR sequences containing moving targets, and named the Video SAR MOT Benchmark (VSMB). Specifically, to mitigate the effects of trailing and defocusing in moving targets, we introduce a line feature enhancement mechanism that emphasizes the positive role of motion shadows and reduces false alarms induced by static occlusions. In addition, to mitigate the adverse effects of target appearance variations, we propose a motion-aware clue discarding mechanism that substantially improves tracking robustness in Video SAR. The proposed model achieves state-of-the-art performance on the VSMB, and the dataset and model are released at https://github.com/softwarePupil/VSMB.