Round up kills just about every thing...but then you will have to dig out the old dead "stumps"...might be cheaper to just dig them out in the first place.
If it is very large a chain and large truck might be required to remove. Just remember to wear long sleeves, heavy duty gloves, and googles if you want to try to hand dig it out. The leaf blades are serrated and stiff and can cause quite a bit of damage to an incautious person. ( Yeah, had to go to the eye doc on that one ! So learn from my mistake:)
It's a chore all right. Please do be careful in doing so.
Depending on the size and maturity of the pampas grass you might have to do a combination of KMS suggestion and Four Season Nursery. Very invasive plant.