Voles? They are rodents, as are mice, but they tunnel and do chew on roots of plants and pull them into their tunnels to have at them.
Moles, on the other hand, which are NOT rodents, sometimes dislodge plants while looking for meaty meals like grubs and worms, but are not specifically herbivores (they will eat a little vegetation, but what you are describing isn’t their style).
Chipmunks (also rodents) can pull off almost any trick imaginable, so I tend to blame them for lots of things. They tunnel, too (bigger hole) and you’d probably know if you had them as they are noisy guys.
Have to agree with ugq– voles are the likely culprits. I have had the astonishing experience of watching a plant shake, shiver, and disappear into a hole at its base, dragged underground like Persephone– a sad sight. Rodent-lovers be warned: I am about to recommend how to get rid of voles in Not Very Nice ways.
I have had a serious problem with voles (and some moles) for years, but considering that I have no deer, few slugs, and no rabbits, either, I figure they are my particular pestilential challenge. In the last few years I hit on a gross but effective way to divert them from their usual runs, allowing my plants to heal and grow strong.
Many areas of the country have had an explosion in rat populations in the last 5 years, and we were among them. I live on a small farm and we began to trap and kill rats to keep them out of our chicken coop and other areas. Knowing that voles are essentially vegetarians, I decided to take advantage of the overflow of rat corpses and bury them in the already conveniently dug vole runs.
This worked, and now that the rat population has reset to normal, I use the carcasses of roasted chickens or other meat scraps. Composting and vole control, along with a nice meal for my plants as the bodies/bones break down– I call this a good solution!
This spring I noticed the vole damage is greatly diminished– the voles seem to have moved on from here, a first in ten years. I don’t think I could possibly have fouled all their runs, it’s probably a cyclical thing, but hey, I’m grateful.