You might want to try out the (included) add-on Bool Tool as demonstrated here that will use one objects mesh, to cut another object, the solution to this question.
In the following I demonstrate using a sphere positioned into a cube. The tool creates the additional required vertices in the sphere in the positions of the same vertices of the sphere and connects the edges to existing edges of the cube:

The wire sphere you see is a duplicate of the cutting/boolean-diff sphere. The cutter is deleted/joined to the cut mesh and cannot be "changed" in the future. I.e., the cut object mesh is permanently changed, so you might want to keep hidden copies of the original (cut and cutter) if you decide to change the sculpting later.
You can also investigate using a mesh as a sculpting tool, although that would also permanently change to sculpted object.