Creating 3D textured meshes using generative artificial intelligence has garnered significant attention recently. While existing methods support text-based generative texture generation or editing on 3D meshes, they often struggle to precisely control pixels of texture images through more intuitive interaction. While 2D images can be edited generatively using drag interaction, applying this type of methods directly to 3D mesh textures still leads to issues such as the lack of local consistency among multiple views, error accumulation and long training times. To address these challenges, we propose a generative point-based 3D mesh texture editing method called DragTex. This method utilizes a diffusion model to blend locally inconsistent textures in the region near the deformed silhouette between different views, enabling locally consistent texture editing. Besides, we fine-tune a decoder to reduce reconstruction errors in the non-drag region, thereby mitigating overall error accumulation. Moreover, we train LoRA using multi-view images instead of training each view individually, which significantly shortens the training time. The experimental results show that our method effectively achieves dragging textures on 3D meshes and generates plausible textures that align with the desired intent of drag interaction.