I would start removing the dam from the bottom up. That will ensure you
1) don't have to try and remove dam walls underwater (which takes longer)
2) You can make sure the water is not running on each level.
On the old Survival world, I made my version of the Nautilas (cf. In pursuit of Dr. Stefan Moriarty... (pic heavy)
). My problem was that it needed to be bigger than the ocean floor, so I had to not only wall off the water, but also had to dig out a big area of the seabed, making sure the water didn't come in from above. Then I had to let it in when finished. The hardest bit was making sure that there was water under the submarine. It was hard to throw water when swimming underwater.