This paper addresses the mitigation of wind turbine clutter (WTC) in weather radar data in order to increase the performance of existing weather radar systems and to improve weather analyses and forecasts. We propose a novel approach for this problem based on signal separation algorithms. We model the weather signal as group sparse in the time-frequency domain; in parallel, we model the WTC signal as having a sparse time derivative. In order to separate WTC and the desired weather returns, we formulate the signal separation problem as an optimization problem. The objective function to be minimized combines total variation regularization and time-frequency group sparsity. We also propose a three-window short-time Fourier transform for the time-frequency representation of the weather signal. To show the effectiveness of the proposed algorithm on weather radar systems, the method is applied to simulated and real data from the next-generation weather radar network. Significant improvements are observed in reflectivity, spectral width, and angular velocity estimates.@en