drag a villager to the sick treebranche , he will use a cloth to bind it off then use a cutting tool to cut the branch and after that use soap to clean the stump

I guess I don't have the right kind of cutting tool because all it ever says is "They need a cutting tool." Could someone please tell me what to do clearly? I can't understand any of these puzzle hints in the forum!

Once you have bound off the branch with the cloth, put the villager on the cutting tool in the lab. It (I think) will say he is pruning the branch or something to that effect. Once that is done, you need to wash the stump with soap to finish cleaning it.

Thank you, that worked. I wish there was a clear, with spoilers, walk through.

Does a new and clean branch ever grow back?

One of the villagers bound off the branch, but I couldnt get him cut it and so now I have a branch with the cloth in it, and none that cuts it. Should it be the same villager? I think he died

After putting a cloth on the branch, you'll need a cutting tool to cut it. So put a villager on the cutting tool in the research lab. Then, put a villager on the soap bars to clean the cut.

If your villager has died and you needed him to complete the puzzle that would mean that you'd never finish it, which seems very unfair. If you are not sure what to use to cut the branch, what do the villagers generally use for cutting? Hint: most people will have solved this as their first puzzle.

Tree limb regrow as shown in the puzzle's picture? That would be neat...

Yes - but not like any tree you ever saw.. New sprout should be be growing from just inside bark, not from core. (I had to remove screenshot as I couldn't figure out how to get it inside 'spoiler'.)

Because the inner wood is actually dead in real trees. lol. How long does it take?

it was after solving puzzle #16

That usually requires a villager to meditate. To make a villager meditate, drag him to the area between the wind flutes. I didn't have to make a villager meditate to complete this puzzle.