Additive manufacturing, particularly in bioprinting, relies on precise slicing algorithms to define printing paths. While traditional planar slicing methods impose geometric limitations, non-planar and multi-axis approaches have emerged to enhance surface quality and manufacturing efficiency. Among these, cylindrical slicing algorithms offer a novel strategy for optimizing material deposition on rotating mandrels. This study aims to implement a novel non-planar slicing algorithm capable of planning extrusion-based printing processes on a rotating mandrel. The algorithm partitions the initial volume into concentric cylindrical layers, each defined by an increasing radius around the mandrel’s core. In the first step, the geometry is sectioned with a plane passing through the mandrel’s axis and then unrolled to produce a volume lying on a planar face. This transformation, applicable to geometries regardless of axial symmetry, facilitates the application of conventional or custom planar/non-planar slicing algorithms. Subsequently, the calculated trajectories are rewrapped, transforming the planar layers into a series of coaxial cylindrical layers aligned around the mandrel. To validate the slicer’s functionality, a rotating spindle was developed and integrated as a fourth motion axis into a previously designed multi-material, multi-scale 3D bioprinter. This system incorporates both an extrusion-based bioprinting unit and a fused filament fabrication unit. The algorithm enables full control over key printing parameters, such as layer thickness, layer width, and infill patterns. Testing on multiple 3D models relevant to biomedical applications demonstrated the algorithm’s robust performance.