In this paper, a novel point cloud segmentation and completion framework is proposed to achieve high-quality leaf area measurement of melon seedlings. In particular, the input of our algorithm is the point cloud data collected by an Azure Kinect camera from the top view of the seedlings, and our method can enhance measurement accuracy from two aspects based on the acquired data. On the one hand, we propose a neighborhood space-constrained method to effectively filter out the hover points and outlier noise of the point cloud, which can enhance the quality of the point cloud data significantly. On the other hand, by leveraging the purely linear mixer mechanism, a new network named MIX-Net is developed to achieve segmentation and completion of the point cloud simultaneously. Different from previous methods that separate these two tasks, the proposed network can better balance these two tasks in a more definite and effective way, leading to satisfactory performance on these two tasks. The experimental results prove that our methods can outperform other competitors and provide more accurate measurement results. Specifically, for the seedling segmentation task, our method can obtain a 3.1% and 1.7% performance gain compared with PointNet++ and DGCNN, respectively. Meanwhile, the R2 of leaf area measurement improved from 0.87 to 0.93 and MSE decreased from 2.64 to 2.26 after leaf shading completion.