- Trees can actually be cut at major branches above ground, provided you can get a woodcutter adjacent to it (I think it has to be some kind of level ground, i.e. not the top of a ramp, so a Down stair on top of an Up stair would work, for instance, or a floor). There's a fair risk the woodcutter will fall, however. Many kinds of fungal trees don't provide any access to their major branches either.
- Saplings can appear if the water level is low enough (<=3/7?) and these saplings can mature even if the water level is raised later.
You can use Immortal-D's cave-in to create a box around the tree, and then pump out the water inside the box. The box has to be wide enough to go outside the most remote twigs of the tree, however, since even the smallest twig will stop a cave-in and suspend the rock on top of it.
So, the best option is to drain the lake, which usually means you have to close off submerged cavern entrances. Those, however, are often made inaccessible by cavern trees... Such cavern trees can be disintegrated (no wood, and an actual hole in the water!) by hitting any part of the tree with a ballista arrow.
When cutting a tree the tree falls away from the woodcutter. If you're able to control which direction a woodcutter comes from, you can maximize the amount that falls on land (this doesn't answer the actual question, but I don't know the answer to that).