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Phased array radars (PARs) are attractive in weather surveillance primarily because of their capability to electronically steer. When combined with the recently developed beam multiplexing (BMX) technique, these radars can obtain very rapid update scans that are useful in monitoring severe weather. A consequence is that the small number of contiguous samples of the time series obtained can be a challenge for temporal/spectral filters used for clutter mitigation. As a result, the accurate extraction of weather signals can become the limiting performance barrier for PARs that employ BMX in clutter-dominated scattering fields. By exploiting the spatial correlation of the auxiliary channel signals, the effect of clutter contamination can be reduced in these conditions. In this paper, three spatial filtering techniques that used low-gain auxiliary receive channels are presented. The effect of clutter mitigation was studied using numerical simulations of a tornadic environment for changes in signal-to-noise ratio, clutter-to-signal ratio, number of time series samples, varying clutter spectral widths, and maximum weight constraints. Since such data are not currently available from a horizontally pointed phased array weather radar, experimental validation was applied to an existing data set from the turbulent eddy profiler, which is a vertically pointed PAR. Although preliminary, the results show promise for clutter mitigation with extremely short nonuniform sampling.