Belt for cutting solid aggregate material such as natural or synthetic stone, include a main belt body comprised of a flexible material and having outer and inner loop surfaces. Multiple drive lugs project from the inner loop surface toward the interior of the loop, and each lug has a belt drive surface generally transverse to the main belt body. Multiple abrasive segments containing diamond particles are partially embedded in the main belt body, so that they form a part of the outer surface of the main belt body. Methods of manufacturing and using the cutting belt are also disclosed.