I've cut a fallen tree into smaller pieces while in the water.
I first tied my cord off at various lengths and secured each to a post on land. Then I tied the last two lengths in the deepest part of water to inflatable rafts - I didn't want the trunks left in the pond, I wanted them out, and they were not sitting flat on the bottom due to a couple branches.
Then I used a hand saw and sawed that bugger at the premarked lengths. Note that I had cords at each end of cut sections, so two cords per section. In this way it was easy to maneuver the trunks in the water. I had no real obstacles in the water preventing me from turning the trunks or pulling toward shore. Also, the rafts definitely helped me.
