Outliers will inevitably creep into the captured point cloud during 3D scanning, degrading cutting-edge models on various geometric tasks heavily. This paper looks at an intriguing question that whether point cloud completion and segmentation can promote each other to defeat outliers. To answer it, we propose a collaborative completion and segmentation network, termed CS-Net, for partial point clouds with outliers. Unlike most of existing methods, CS-Net does not need any clean (or say outlier-free) point cloud as input or any outlier removal operation. CS-Net is a new learning paradigm that makes completion and segmentation networks work collaboratively. With a cascaded architecture, our method refines the prediction progressively. Specifically, after the segmentation network, a cleaner point cloud is fed into the completion network. We design a novel completion network which harnesses the labels obtained by segmentation together with farthest point sampling to purify the point cloud and leverages KNN-grouping for better generation. Benefited from segmentation, the completion module can utilize the filtered point cloud which is cleaner for completion. Meanwhile, the segmentation module is able to distinguish outliers from target objects more accurately with the help of the clean and complete shape inferred by completion. Besides the designed collaborative mechanism of CS-Net, we establish a benchmark dataset of partial point clouds with outliers. Extensive experiments show clear improvements of our CS-Net over its competitors, in terms of outlier robustness and completion accuracy.