We introduce a robust estimation procedure that is based on the choice of a representative trimmed subsample through an initial robust clustering procedure, and subsequent improvements based on maximum likelihood. To obtain the initial trimming we resort to the trimmed k-means, a simple procedure designed for finding the core of the clusters under appropriate configurations. By handling the trimmed data as censored, maximum likelihood estimation provides in each step the location and shape of the next trimming. Data-driven restrictions on the parameters, requiring that every distribution in the mixture must be sufficiently represented in the initial clustered region, allow singularities to be avoided and guarantee the existence of the estimator. Our analysis includes robustness properties and asymptotic results as well as worked examples.