This work proposes a novel approach to segmenting randomly stacked objects in unstructured 3D point clouds, which are acquired by a random-speckle 3D imaging system for the purpose of automated object detection and reconstruction. An innovative algorithm is proposed; it is based on a novel concept of 3D watershed segmentation and the strategies for resolving over-segmentation and under-segmentation problems. Acquired 3D point clouds are first transformed into a corresponding orthogonally projected depth map along the optical imaging axis of the 3D sensor. A 3D watershed algorithm based on the process of distance transformation is then performed to detect the boundary, called the edge dam, between stacked objects and thereby to segment point clouds individually belonging to two stacked objects. Most importantly, an object-matching algorithm is developed to solve the over- and under-segmentation problems that may arise during the watershed segmentation. The feasibility and effectiveness of the method are confirmed experimentally. The results reveal that the proposed method is a fast and effective scheme for the detection and reconstruction of a 3D object in a random stack of such objects. In the experiments, the precision of the segmentation exceeds 95% and the recall exceeds 80%.