rDave, chances are you have African Mahogany, which is very grainy. It can leave rough edges. I prefer genuine Honduras Mahogany. It will leave a very smooth, almost shiny cut edge with absolutely no sanding necessary.
I use mainly hardwoods like genuine Mahogany, Cherry, Maple, Red Oak, and Maple. I also use Sapele, which is a good substitute for genuine Mahogany. All of these woods mentioned will leave very smooth cut edges.
I do use Baltic birch plywood for portraits and such.