The shoots will only flower once and then decline over the next one-three years. So if a stem had flowered you can cut it to the ground. However, the shoots normally do not flower in their first year either (at least not in my area) and need a second year to flower. So if you cut off all shoots every year you will probably never see a flower. Clumps can be divided with an axe, crowbar, elephant or dynamite, especially if you live in an area with heavy soils. Don't worry it does not seem to be prone to rotting, to the contrary.