My first question is what do you mean by "mahogany?" The word is now used to describe quite a few different genus and species of wood, and the working characteristics can vary widely. In my experience, true mahogany (Swietenia macrophylla, Swietenia mahogani) are wonderful woods to work with and tend to tear out very little. With a ribbon stripe figure, there will be reversing grain, and some tear out may occur.
African mahogany (Khaya ivorensis) is notoriously difficult to plane because of the reversing and interlocked grain. I tend to leave it oversized, and then sand or scrape it to the desired dimension.
Other species like sapele and andiroba are sometimes sold as mahogany as well.
Finally, Phillipiine mahogany, which is actually better called red luan, is almost impossible to achieve any kind of smooth surface. It fuzzes up no matter what you do. I doubt that this is what you are talking about.
Regardless of which of these woods you are actually dealing with, the advice of the previous posters is good. Unfortunately, if you have stock with reversing grain as in the ribbon stripe figure, each time you reverse the feed direction in the jointer or planer, the grain that you just smoothed in the last pass will tear out. Very light cuts, very sharp blades, and sanding will be what is required.
Hope this helps.
Matt