Sounds like multiple critters, although if I had to pick just one, I would say squirrels. They like to bury stuff. They're also big enough to uproot a small plant. And ubiquitous.
Chipmunks dig like crazy and they like getting into pots and digging there too. They generally don't pull plants out but a hole or two in the right place can topple them.
They are persistent, and climb as well as they dig.
Deer can, and will, eat almost anything and they often pull when they eat.
Groundhogs will eat plants too, and although they dig a hole or two they are generally for homes. They don't dig a bunch of little holes all over the place like chipmunks do.
I had to put screens over the dirt in my outdoor pots to keep the monks from digging in them.
I've also had success (so far) in mixing dried pepper flakes into the soil to discourage digging in selected areas. I don't think the flakes will harm plants, seems like it shouldn't, anyway.
Good luck, try to dissuade rather than kill, if possible. Your current garden visitors will adapt, killing something just means a n00b will move in to take its place & you'll have to start all over again. Besides all the other bad shit that goes along (imo) with killing stuff.