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The tea industry is one of China’s most important industries. The picking of famous tea still relies on manual methods, with low efficiency, labor shortages and high labor costs, which restrict the development of the tea industry. These labor-intensive picking methods urgently need to be transformed into intelligent and automated picking. In response to difficulties in identification of tea buds and positioning of picking points, this study took the one bud with one leaf grade of the Fuyun 6 tea species under complex background as the research object, and proposed a method based on deep learning, combining object detection and semantic segmentation networks, to first detect the tea buds, then segment the picking area from the tea bud detection box, and then obtain the picking point from the picking area. An improved YOLOX-tiny model and an improved PSP-net model were used to detect tea buds and their picking areas, respectively; the two models were combined at the inference end, and the centroid of the picking area was taken as the picking point. The YOLOX-tiny model for tea bud detection was modified by replacing its activation function with the Mish function and using a content-aware reassembly of feature module to implement the upsampling operation. The detection effects of the YOLOX-tiny model were improved, and the mean average precision and recall rate of the improved model reached 97.42% and 95.09%, respectively. This study also proposed an improved PSP-net semantic segmentation model for segmenting the picking area inside a detection box. The PSP-net was modified by replacing its backbone network with the lightweight network MobileNetV2 and by replacing conventional convolution in its feature fusion part with Omni-Dimensional Dynamic Convolution. The model’s lightweight characteristics were significantly improved and its segmentation accuracy for the picking area was also improved. The mean intersection over union and mean pixel accuracy of the improved PSP-net model are 88.83% and 92.96%, respectively, while its computation and parameter amounts are reduced by 95.71% and 96.10%, respectively, compared to the original PSP-net. The method proposed in this study achieves a mean intersection over union and mean pixel accuracy of 83.27% and 86.51% for the overall picking area segmentation, respectively, and the detecting rate of picking point identification reaches 95.6%. Moreover, its detection speed satisfies the requirements of real-time detection, providing a theoretical basis for the automated picking of famous tea.