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LiDAR-based 3D object detection is an indispensable task in advanced autonomous driving systems. Though impressive detection results have been achieved by superior 3D detectors, they suffer from significant performance degeneration when facing unseen domains, such as different LiDAR configurations, different cities, and weather conditions. The mainstream approaches tend to solve these challenges by leveraging unsupervised domain adaptation (UDA) techniques. However, these UDA solutions just yield unsatisfactory 3D detection results when there is a severe domain shift, e.g., from Waymo (64-beam) to nuScenes (32-beam). To address this, we present a novel Semi-Supervised Domain Adaptation method for 3D object detection (SSDA3D), where only a few labeled target data is available, yet can significantly improve the adaptation performance. In particular, our SSDA3D includes an Inter-domain Adaptation stage and an Intra-domain Generalization stage. In the first stage, an Inter-domain Point-CutMix module is presented to efficiently align the point cloud distribution across domains. The Point-CutMix generates mixed samples of an intermediate domain, thus encouraging to learn domain-invariant knowledge. Then, in the second stage, we further enhance the model for better generalization on the unlabeled target set. This is achieved by exploring Intra-domain Point-MixUp in semi-supervised learning, which essentially regularizes the pseudo label distribution. Experiments from Waymo to nuScenes show that, with only 10% labeled target data, our SSDA3D can surpass the fully-supervised oracle model with 100% target label. Our code is available at https://github.com/yinjunbo/SSDA3D.