Hello,
Below is what I found on-line. 
Two-spotted mites – Not truly insects, two-spotted mites are tiny plant-feeding arachnids. You may notice fine webbing collecting on your yucca when they start to show signs of infestation, but it’s more likely that you’ll not notice anything different until the plant is having serious problems thriving. You can suppress mites by increasing the humidity around your yucca, but this could encourage fungal disease instead. For best results, smother the mites with neem oil or an insecticidal soap applied several times according to the package directions.
Let us know if you have any further questions.
Happy Gardening,
CSU Ext Master Gardeners

Can you identify this bug (moth?) on my yucca? It is less than a centimeter long. I suspect it is the one causing this damage. Should I dig out the yucca and toss it and plant one of the healthy pups in its place? What should I do to prevent recurrence ?

Thanks!

Hello,
I forgot to provide the website I quoted from:
https://www.gardeningknowhow.com/ornamental/foliage/yucca/yucca-plant-bugs.htm
Best,
Boulder County Master Gardeners