The paper proposes a partition-based topology optimization approach for multi-axis additive manufacturing(AM), aiming to fully leverage its advantages in dynamic build orientation adjustment and region-specific manufacturing. To address the challenge of decomposing the evolving structural layouts, an implicit decomposition method based on Voronoi diagrams is introduced, which employs a Softmax function combined with Heaviside projection. This Voronoi-based approach ensures full coverage of the design domain and hence provides stable partitioning for arbitrary geometries. Complex volume decomposition is achieved by controlling a small number of seed points within the Voronoi diagram. To prevent unrealistic diffuse interfaces between partitions, a Kreisselmeier–Steinhauser(KS) aggregation-based distance constraint is imposed on the seed points. By integrating the volume decomposition with the spatial gradient of the structural density field, global overhang constraints are formulated for individual partitions. We then optimize the topological layout, partitions and their associated build orientations simultaneously to obtain self-supported design in density-based topology optimization. To validate the effectiveness of the proposed method, several 2D and 3D numerical examples are studied. The influence of partitioning parameters, including the initial build orientations in partitions and the number of partitions, on the optimized design is investigated. Numerical results demonstrate that the proposed method yields reasonable partitioned designs, with the overhang surfaces in the partitions effectively controlled.