This reply is several months after the original post but since I have experience with all the animals on Triloba Tracker's suspect list and suggested by others, I thought I would chime in.
The likeliest candidates are possums or armadillos. Both will make a mess of the ground until they find whatever invertebrate life they are after. If you have a fully and securely fenced-in yard, then it is a possum as they can climb anywhere.
Groundhogs only dig for their burrows; they are herbivores. Supposedly, they will eat blackberries. I am not sure whether they will eat the plant, fruit, or both, but I have resident groundhogs in my yard which I have observed on multiple occasions passing by my blackberries without so much as a glance at them. Perhaps they simply like the many native wildflowers in my yard better.
Raccoons are too lazy to dig, particularly urban/residential area raccoons. Yes, they can dig when they are in the "wild." They will go after trash, pet food, fruit, bird seed, and many other things before they will work for their food by digging.
Voles only dig very tiny holes as access to their burrows. They eat grass and wildflowers; I have never had a problem with them attacking trees or any food plants. Again, while I have many voles, I also have many wildflowers for them to eat.
Field mice are a similar story to voles.
Chipmunks are diurnal. They make a mess but, like squirrels, dig holes rather than trenches. I cannot stand chipmunks or squirrels. Those two animals, along with raccoons, are the only animals I consider to be pests due to their destructiveness, but that is as much to do with their gnawing as their digging.
Foxes will dig if they are after prey, like a vole or mouse, or are digging their den but otherwise will not dig. They are rarer than they used to be in the southeastern United States; they have been displaced by coyotes. If you have foxes in your area, they will probably prey on the squirrels and chipmunks. I have watched foxes hunt squirrels so masterfully that those foxes never had any need to dig for their dinner.
There are no badgers in Middle Tennessee. Like where I live, Middle Tennessee is too far south and east to be in their range. If we had badgers, they would probably make a mess of the place with their digging, but it would likely be in the form of big tunnels.
I hope this helps anyone who is dealing with digging animals.