Owing to human labor shortages, the automation of labor-intensive manual waste-sorting is needed. The goal of automating waste-sorting is to replace the human role of robust detection and agile manipulation of waste items with robots. To achieve this, we propose three methods. First, we provide a combined manipulation method using graspless push-and-drop and pick-and-release manipulation. Second, we provide a robotic system that can automatically collect object images to quickly train a deep neural-network model. Third, we provide a method to mitigate the differences in the appearance of target objects from two scenes: one for dataset collection and the other for waste sorting in a recycling factory. If differences exist, the performance of a trained waste detector may decrease. We address differences in illumination and background by applying object scaling, histogram matching with histogram equalization, and background synthesis to the source target-object images. Via experiments in an indoor experimental workplace for waste-sorting, we confirm that the proposed methods enable quick collection of the training image sets for three classes of waste items (i.e., aluminum can, glass bottle, and plastic bottle) and detection with higher performance than the methods that do not consider the differences. We also confirm that the proposed method enables the robot quickly manipulate the objects.