This paper presents a novel framework that integrates topology optimization (TO) and deep learning (DL) to generate high-performance structures suitable for multi-axis machining. Within the proposed framework, DL is built on the pix2pix network, with the conditional channel used to determine the tool shape and feed direction in multi-axis machining. This DL model will be trained using our own generated dataset on TO for multi-axis machining. Then, users can customize tool dimensions and machining orientations of the multi-axis machining operation and specify the design boundary and loading conditions as input. The DL model will rapidly generate a near-optimized structure, which subsequently serves as the starting point for further optimization. Ultimately, a topology-optimized structure that meets the tailored requirements is apt for multi-axis machining and can be finalized with only a few iterations. 2D and 3D numerical examples for heat conduction problems are studied to prove the effectiveness of the proposed method, validating improved structural performance and optimization efficiency compared to conventional TO for multi-axis machining.