For making an extrusion to divide the solid into separate solid chunks you could try doing a type of "radial extrusion" by going to the top view and using Transform > Scale > Scale2d to make 2 copies (ctrl click on the final pick for scale to make a copy) and then loft between those to make this type of thing:



That can then divide a solid like this:



To make a solid cutting tool to cut your original solid up:





This is probably not going to be very good for filleting though, although maybe it would get simplified some too by having ends be perpendicular to the ending edges.

- Michael