I don't remember if real cold area ponders leave the pots in the pond, but I certainly do in zone 7. I divide them in spring and either retain them or discard. As mentioned recently, I don't worry much about bottom crud, but I have a stream that filters out much of that crud over time. In any case, I'm sure that you can remove pads as they turn yellow and no longer provide energy to the plant. One point is that pulling on a yellow pad will normally remove the whole stem so there should be nothing to cut.

I had the same problem with Water Iris. I took some to my Mom who has a larger pond, but the rest I had to throw away. I couldn't find anyone that needed them even free, and didn't want to mess with posting them on Craigslist.

I agree with chas045, leave them in the pond. I'm in Michigan (5b-6a) and they did fine last year. Cut the stems down to the tuber (or as far down as you can reach) and divide in Spring when they're in the growing stage.

I have irises in pots that I remove from the pond, cut back and bury ground level on the side of my house. I put them back in the pond in the Spring when the new growth is 3-5" high.