You'll definitely need a hacksaw. It's much easier and safer with a new, sharp blade with the finest teeth that you can find - you'll want to avoid ripping the CF strands. Better yet, buy a carbide hacksaw blade if you have a few quid to spare. Also just remove the fork entirely to make sure you get a straight cut. You can get fancy cutting guides, or just do as I did and use two hose clamps padded with electrical tape and spaced a few millimetres apart.
Use even and smooth strokes, be patient and let the blade do the work, and for god's sake don't try to break of the last little connected bit by hand.
If you do end up some loose strands after cutting, rub them away with fine sandpaper, don't pull on anything. Carbide blades will not have this problem.