The machining features of mechanical parts not only determine their functional and structural uniqueness but also embody rich process knowledge, which directly affects the feasibility of manufacturing. Current research on machining features predominantly focuses on the identification of geometric structures, while overlooking the implicit process knowledge. The disconnect between feature modeling and actual machining limits the advancement of manufacturing systems toward intelligence and flexibility, making it difficult to meet the demands of high-mix, low-volume customized production. To address the disconnect between geometric structure and process knowledge, this paper introduces the concept of machining features and proposes a machining feature recognition and embedding model based on graph convolutional networks, named MFRed-Net. Specifically, this paper classifies machining features into five categories based on the impact of their structural closed and through on process knowledge, and extracts feature subgraphs of surface attributed graphs to represent machining features. MFRed-Net reformulates the feature recognition task as a multi-class classification task for node and a binary classification task for edge, with a hybrid cross-entropy loss function. Finally, machining feature embeddings are obtained through pooling operations on the feature subgraphs. A dynamic programming algorithm is then applied to evaluate the accuracy of recognition. Experimental results show that the MFRed-Net achieves a per-face accuracy of 95.6%, outperforming baseline by more than 4.9%. Additionally, the model reaches 95.0% in the feature recognition, and its effectiveness and robustness were validated through ablation experiments.