Clipping is an important operation in the context of direct volume rendering to gain an understanding of the inner structures of scientific datasets. Rendering systems often only support volume clipping with geometry types that can be described in a parametric form, or they employ costly multi-pass GPU approaches. We present a SIMD-friendly clipping algorithm for ray traced direct volume rendering that is compatible with arbitrary geometric surface primitives ranging from mere planes over quadric surfaces such as spheres to general triangle meshes. By using a generic programming approach, our algorithm is in general not even limited to triangle or quadric primitives. Ray tracing complex geometric objects with a high primitive count requires the use of acceleration data structures. Our algorithm is based on the multi-hit query for traversing bounding volume hierarchies with rays. We provide efficient CPU and GPU implementations and present performance results.