Clearing a bed of iris

[gardenymph]

I have a bed filled with hundreds of irises. I would like to clear it out but pulling them up doesn't seem to be a permanent solution as they come back. Short of a chemical solution, is there a good way to clear them out. I was thinking about pulling them up and then covering with landscaping cloth and then covering that with mulch. Any thoughts??

[Trollskogen]

Have you just tried to pull out the plant by the leaves instead of digging up the rhizomes (roots)?