I've never cut Kevlar with a diamond blade, but have used a bandsaw, with blade teeth pointing up (not down) as recommended on the DuPont website:
A conventional steel blade with 14 to 22 teeth per inch is fine for composites containing KEVLAR brand fiber. The teeth can be set in either raker or standard position. To get the best results, use a cutting speed between 3,000 and
6,000 FPM and a slow feed rate of about 1-2 FPM. In most cases it is best to mount the saw blade upside down so that the teeth are pointing up. This way the teeth will act as if they were knives and give a less aggressive, cleaner cut. With a standard shop mechanic's honing stone, hone a new blade before using it to remove any burrs left by the manufacturing process. Burrs catch the fibers and pull them, causing the fibers to fuzz. Backing will improve cutting quality. Masking tape can also serve as a backing. Water coolant is okay for heavy cuts.
Call 1-800-4 KEVLAR for additional advice.