The tree in the poem heals itself by "absorbing years of sunlight, air, water." Even if attacked, hacked, and chopped, the tree will heal itself by drawing upon the earth and its surrounding environment. It will absorb the sun's energy and water from the soil.
The speaker says that the only way to kill the tree is to pull out the root, "Out of the anchoring earth." The implication, therefore, is that, if the root is not pulled out, then it will be through the root that the tree continues to heal itself. It will continue to absorb energy from the soil.
The whole poem is in part a celebration of the strength and endurance of trees. They survive despite being hacked at and chopped at, despite being scorched and choked. It takes a huge effort to kill a tree, which in turn implies an attack on those who make the effort nonetheless.