Clutter suppression is a key step for efficient detection of moving targets and accurate estimation of their parameters. Current clutter suppression approaches are available for the case in which clutter signals of each channel are free from Doppler ambiguity. However, for a multichannel high-resolution wide-swath (HRWS) synthetic aperture radar (SAR) system, the received echoes of each channel suffer Doppler ambiguity, thus current clutter suppression approaches may not perform well. To address this issue, the signal models of stationary and moving targets with Doppler ambiguity should be derived. This paper presents their analytical models in the complex image domain by two-dimensional azimuth compression, from which the linear coupling of a moving target induced by radial velocity can be eliminated, and thus signal-to-noise ratio loss caused by this linear coupling can be avoided. Considering that there is a difference between stationary and moving targets in the complex image domain, a clutter suppression approach for a multichannel HRWS SAR system is proposed. The simulated results and real data processing results both validate the proposed approach.