If that is spatterdock I had an old pond that I refurbished that was nearly covered in it.
I was amazed when the dozer started pushing the muck out of the bottom of the pond how big the rhizomes of this plant get. Some were nearly as big as my arm and several feet long down into the muck. I had rhizomes laying all over the bank. Many tried re-sprouting even after laying in the sun for weeks and seemingly dried out.
My point is, with the nutrients stored in these rhizomes, it would take removal of the tops many, many, many times before the root could possibly be starved out to the point it could no longer send up new shoots.
So in my estimate, the only real way to get rid of the stuff would be with a systemic herbicide like Bill Cody suggests to go after the rhizomes in the bottom of the pond.
After seeing what grows beneath the surface, cutting the tops off to try and get rid of it looks like it would be an exercise in futility to me. Only other alternative is do like I did, drain the pond and clean all the muck and rhizomes completely out.
