I would start by pruning off the small twig like branches, Just cut off branches untill you start hitting things 3/4 - 1" in thickness, leave these alone.
Save everything you clip off, those little tiny things are usefull for nanos
Generally I think you'd want to just cut where it attaches to a larger branch.
Then just start cutting branches off the main branches untill you're left with the thickest branches, Then cut these off from the trunk, leave as many inches as possible above the ground.
And you'll definately want to save the roots and trunk, When dug up, they look really, really cool. To me anyway.
After that, you'll probably just want to let them die off and bake over the summer. I'm not entirely sure what kind of curing or ageing it needs to go through, but I'm pretty sure you don't want green wood.
I would atleast wait until the red bark could be easily stripped off.
Worry about cleaning after you've let them bake
Would you happen to have a larger version of that picture? I could mark off where I would cut if you'd like.
Wabi Kusa is just an Aquascape Katamari