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Additive manufacturing is capable of forming part solids from a digital model of the workpiece, which often needs to be sliced due to the nature of the process of stacking materials layer by layer. Previous algorithms require more time to order the intersection points during slicing and only consider a fixed axis vector as the slicing direction. With the increasing complexity of the workpiece model, it is necessary to improve the efficiency of the slicing algorithm, and the given slicing direction should be flexible and convenient. Therefore, this paper proposes an efficient algorithm for slicing in any direction using the shared edges of adjacent triangles. Firstly, the model can be efficiently sliced in any direction by custom vectors, which is convenient for process validation; secondly, the shared edges of neighboring triangular facets intersecting the plane need to be calculated only once to reduce redundant calculations; finally, the ordered intersections of the constructed inner and outer contours are directly outputted without any additional sorting to reduce the running time. The experimental results show that compared with other algorithms, the proposed algorithm can improve the execution efficiency and eliminate the constraint that the slicing direction is fixed on the Z-axis, which is of application value and reference significance for additive.