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Data heterogeneity is an intrinsic property of recommender systems, making models trained over the global data on the cloud, which is the mainstream in industry, non-optimal to each individual user's local data distribution. To deal with data heterogeneity, model personalization with on-device learning is a potential solution. However, on-device training using a user's small size of local samples will incur severe overfitting and undermine the model's generalization ability. In this work, we propose a new device-cloud collaborative learning framework, called CoDA, to break the dilemmas of purely cloud-based learning and on-device learning. The key principle of CoDA is to retrieve similar samples from the cloud's global pool to augment each user's local dataset to train the recommendation model. Specifically, after a coarse-grained sample matching on the cloud, a personalized sample classifier is further trained on each device for a fine-grained sample filtering, which can learn the boundary between the local data distribution and the outside data distribution. We also build an end-to-end pipeline to support the flows of data, model, computation, and control between the cloud and each device. We have deployed CoDA in a recommendation scenario of Mobile Taobao. Online A/B testing results show the remarkable performance improvement of CoDA over both cloud-based learning without model personalization and on-device training without data augmentation. Overhead testing on a real device demonstrates the computation, storage, and communication efficiency of the on-device tasks in CoDA.