Ask Mr. Smarty Plants

In future, promise to keep your weed wacker well away from the yucca, tree bark or any plant you are interested in keeping. Those things can easily damage a plant that will leak sap and invite insects to come feed on it, often resulting in disease and/or death of the plant.

Extracted from a previous Mr. Smarty Plants answer on trimming yucca:

Yes, you can certainly prune off the damaged blades, and do so clear back to the trunk. If the damaged blades are all close to the ground, just trim evenly all the way around, which will make the trunk of the yucca look longer, and keep lower leaves out of the range of the machinery (which you promised not to use around there again.)

For this, you will need long pruning shears, and wear long sleeves and pants, leather gloves and a pair of goggles to protect your eyes. Be careful how you discard the trimmed-off portions, they will poke right through a plastic trash bag, but you can find heavy duty paper trash bags that should suffice. And don't try them in a compost pile-it takes them a long time to decompose, and they maintain their stickeriness throughout.