Unsupervised clustering is a powerful machine-learning technique widely used to analyze high-dimensional biological data. It plays a crucial role in uncovering patterns, structures, and inherent relationships within complex datasets without relying on predefined labels. In the context of biology, high-dimensional data may include transcriptomics, proteomics, and a variety of single-cell omics data. Most existing clustering algorithms operate directly in the high-dimensional space, and their performance may be negatively affected by the phenomenon known as the curse of dimensionality. Here, we show an alternative clustering approach that alleviates the curse by sequentially projecting high-dimensional data into a low-dimensional representation. We validated the effectiveness of our approach, named automated projection pursuit (APP), across various biological data modalities, including flow and mass cytometry data, scRNA-seq, multiplex imaging data, and T-cell receptor repertoire data. APP efficiently recapitulated experimentally validated cell-type definitions and revealed new biologically meaningful patterns.