First you'll need to get the Gym Badge from the Azalea Gym which will allow you to use the move Cut outside of battle.
Next you need to get the Cut HM. To get it, go to Ilex Forest and talk to a man next to a tree with can be Cut. He'll say he lost his boss' Farfetch'd, so look around and herd the bird back to him by pressing 'A' when you reach it. When you're done, the guy will give you Cut and you can get past the tree.