In semiconductor manufacturing, a wafer bin map (WBM) is a map that consists of assigned bin values for dies based on wafer test results (e.g., value 1 for good dies, and value 0 for defective dies). The bin values of adjacent dies are often spatially correlated, forming some systematic defect patterns. These non-random defect patterns occur because of assignable causes; therefore, it is important to identify these systematic defect patterns in order to know the root causes of failure and to take actions for quality management and yield enhancement. In particular, as wafer-fabrication processes have become more complicated, mixed-type defect patterns (two or more different types of defect patterns occur simultaneously in a single wafer) occur more frequently than in the past. For more effective classification of wafers according to their defect patterns, mixed-type defect patterns need to be detected and separated into several clusters of different patterns; subsequently, each cluster of a single pattern can be matched to a well-known defect type (e.g., scratch, ring) or it may indicate the emergence of a new defect pattern. There are several challenges to be overcome in the detection and clustering of mixed-type defect patterns. These include: 1) the separation of random defects from systematic defect patterns, 2) determining the number of clusters, and 3) the clustering of complex shapes of defect patterns. To address these challenges, in this paper, we propose a new framework for detecting and clustering mixed-type defect patterns. First, we propose a new filtering method, called the connected-path filtering method, to denoise WBMs. Subsequently, we adopt the infinite warped mixture model for the clustering of mixed-type defect patterns; this model is flexible in its ability to deal with complex shapes of defect patterns, and furthermore, the number of clusters does not need to be specified in advance, but is automatically determined simultaneously during the clustering procedure. We validate the proposed method using real data from a semiconductor company. The experimental results demonstrate the effectiveness of the proposed method in estimating the number of underlying clusters as well as in the clustering of mixed-type defect patterns.