We need to know some 'history' re the African Mahogany.
Did you allow it to stabilize by living in your shop a few weeks?
Being a 'novice', the answer is likely no.
When bringing a piece from one environment(lumber yard) to another(your shop), the wood needs to gain moisture stabilization prior to being cut(especially ripping).
Another thing is ripping releases internal tension that is worse when not stabilized.
It is folly to think gluing and clamping in a different from unclamped shape will succeed in the long run.
If you are making an end grain cutting board, are not the 'pieces' relatively short?
Goldie(Bought New SN 377425)/4" jointer/6" beltsander/12" planer/stripsander/bandsaw/powerstation /Scroll saw/Jig saw /Craftsman 10" ras/Craftsman 6" thicknessplaner/ Dayton10"tablesaw(restoredfromneighborstrashpile)/ Mark VII restoration in 'progress'/ 10E(SN E3779) restoration in progress, a 510 on the back burner and a growing pile of items to be eventually returned to useful life. - aka Red Grange