When a compressor is throttled to the near stall point, rotating instability (RI) is often observed as significant increases of amplitude within a narrow frequency band which can be regarded as a pre-stall disturbance. In the current study, a single compressor rotor row with varying blade tip clearance (1.3%, 2.6% and 4.3% chord length) was numerically simulated using the zonal large eddy simulation model. The mesh with six blade passages was selected to capture the proper dynamic feature after being validated in comparison to the measured data, and the dynamic mode decomposition (DMD) approach was applied to the numerical temporal snapshots. In the experimental results, RIs are detected in the configurations with middle and large tip gaps (2.6% and 4.3% chord length), and the corresponding characterized frequencies are about 1/2 and 1/3 of the blade passing frequency, respectively. Simulations provide remarkable performance in capturing the measured flow features, and the DMD modes corresponding to the featured RI frequencies are successfully extracted and then visualized. The analysis of DMD results indicates that RI is essentially a presentation of the pressure wave propagating over the blade tip region. The tip leakage vortex stretches to the front part of the adjacent blade and consequently triggers the flow perturbations (waves). The wave influences the pressure distribution, which, in turn, determines the tip leakage flow and finally forms a loop.