If you have reached that part during the "Lost City"quest, you are meant to "Kill" a tree spirit then killing it will allow you to cut down a branch from the dramen tree.
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get any jewels and a chisel and with the right crafting level you can cut them!
You take or buy a chisel and have to have a high crafting level and then just cut it.
small trees are cut you can usually find them if there is a place you have to go but there is a fence with a tree in an opening use cut on the tree to use cut teach it to one of your Pokemon and walk up to the tree and press A it will say would you like to cut the tree say yes.
If there is a pokemon in your party that can use Cut and you have the second badge then face a tree that can be Cut down press A on it then press A on YES to cut the tree alternatively you can open the pokemon screen and select your pokemon and press A on Cut.
using cut