Many plants will create two offshoots where you cut, so you can increase the density of the plant doing this. The problem is, when those reach the surface, usually it has become too hard to tell the plants apart without pulling them up. If you cut blindly you tend to cut the offshoots and eventually end up with really weird stems. At that point, you may as well pull them up, cut off the good stems and plant them and dump the bases as by now they have lose their leaves and become all rooty. Nothing wrong with this, but it doesn't look as good until it grows back in. And you end up replanting the new plants for days until they form roots to hold them down.
I guess my point here is that cutting lower is better, but no so low that it won't get any light. If you cut too high, it'll branch there and you'll end up cutting the whole thing off before too long. In my experience, planting branched stems is harder because the extra stems add buoyancy and they tend to pull themselves up constantly.
With some plants, you also have the option of letting them grow "emergent." If the stems are strong enough they will grow up and out of the water. For a while the above-water leaves will wilt and look ratty, but eventually it will grow leaves that can grow without water. Most plants that grow emersed will form different leaves out of the water than in it, mainly due to the difference needed to support the plant structurally. Once the emergent part gets too large you can cut it off and plant it in a bog like I have above my tank or similarly wet environment. The last plant I did that to wilted at first, but came back. incidentally, most plants you buy in stores have been grown emmersed because they grow faster this way. That's why they might look different in the store than you see in photos. It's also why they will often drop all their leaves when you put them in your tank, because they need to grow new leaves for underwater growth. Another reason why buying from hobbyists via sites like this is preferable.
Michael