how do i polish the edge of a granite tile after cutting it?

my daughter recently purchased a home that was built in the 1960's which has terrazzo floors some of which had been covered with carpet which was really dirty so we removed it only to find that some of the old pad had been glued down with what looks like asphalt based mastic we have scraped up most of this with razor scrapers and are wondering how to remove the remove the residue so that the terrazzo will be usable. we do have access to a comericial buffer with stripping pads ect. i know that terrazzo is routinely stripped and resealed but do not know if this will remove the residue or not. gerge