You don't want to cut down culms if you don't have to. It might make it easier for you, but it could be a couple of years before the transplanted rootball starts putting out decent size culms again.

An important issue is timing. I don't know what shooting season is for your bamboo in your Zone, but you don't want to divide any kind of bamboo while it's sending up new shoots.

As far as the actual division, clumpers have very tough, dense root systems, which always makes dividing a challenge. Pick out a logical area for a division, and then you will need to try to saw (SawzAll, root pruning saw, etc.) down through the rootball to isolate that division...then pry it out with a demolition bar to free it. The last time I divided a clumper it was almost impossible to saw through and we finally managed to get through after about 1/2 hour of pounding on a sharpened spade with a hand sledge in order to "chisel" through!