Yes they can be divided. If the plant has multiple stems coming out of the ground these usually will develope their own root systems. These can be divided and planted separately. Clematis don't like to be divided though. It can take another 3-5 years for it to reestablish and bloom well again. Jackmanii is a very common cultivar. It you want another one I would just pick up another one at a fall clearance sale and leave your mature one alone.