Burn it out if you can,then its much easier to dug out what's left,wait till there a good amount of rain due and cover the clump before the rain to keep it dry that way you can burn it once every thing around it becomes green
I have previously found the combination of a machete (very satisfying!!) and digging out the base to work well. It's hard work, but much less daunting once it is macheted down to size.
On a commercial scale I have used the machete technique (a scrub cutter or weed eater would work too) in combination with application of Vigilant gel to the cut base.
Be aware when cutting that many beasties like to nest in Pampas- from wetas and spiders to ducks and (once) saddlebacks!