You need the axe. A torch or the hammer won't clear roots, and the axe is a long way in: past the spider prison, through the sewers and into a crypt.
Where do you get the axe to break roots?
In the crypt beyond the flooded part of the sewers. One pair of players took about 12 hours to find it, so don't worry if you've been stuck on roots for a while.
- Go through the spider prison and down into the sewers. Past the prison, a new section of the sewers opens up.
- Get past the slime. It sits on the way to the water controls.
- Turn all the cranks with the grappling hook. That lowers the water in this part of the sewers.
- Head into the crypt that opens up and search it for the axe.
If you don't have the grappling hook yet, that's the thing to get first. The cranks are out of reach without it.
Then go back to every root wall you skipped. A lot of the map opens up once they're gone.
How do you cut vines?
You don't need a tool. Vines are something you pick up by hand, even though they look like decoration at first. Walk up to them and grab them.
Hanging wall vines can also be climbed. Loose vines go into rope (two vines and a stick) and into the Pouch at the workbench.