You have to get the HM01(cut) , teach it to a Pokemon and when you're facing the a tree to cut down open the Pokemon team menu and click on the Pokemon that knows cut and select the cut option. You also need the second gym badge
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Teach HM Cut to a Pokemon and use it on the tree.
In Eterna city. First you have to fight the gymleader at Eterna. Then teach one of your Pokemon cut. Then above the Pokemon center there's a blue building with three breakable trees. Use cut on those trees. Then go in the building. In the building fight commander Jupiter. After that you save the bicycle guy. Then get out of the building. Then go to the building of the bicycle guy which is brown in Eterna. It has bicycles by it.
First teach your Pokemon cut then you must beat the 2nd gym leader now press Start and press A on Pokemon your Pokemon will be displayed choose the Pokemon you taught Cut to and press A on it a menu will show up with diffrent commands choose Cut now your Pokemon will use cut.
You get HM01 Cut from Ilex Forest. Use that to cut down trees.
bidoof and bibarel can cut trees