I have a 3-mth-old lab cross pup and she has recently decided that she enjoys tearing up chunks of yard -- the bigger, the better. She will just lay and gum the whole mess until she loses interest and pulls up another chunk. She doesn't even eat it all! She seems to have gotten the idea from my housemate's 7-mth-old Jack Russel. Unfortunately, my pup being a bit bigger and stronger tends to rip up bigger clods. I monitor them outside as much as possible, mixing in sitting outside with periodically looking out the window. But, other than saying "no" in a determined voice and standing over the spot so that they are forced to move, I am not sure how to handle the problem. I rent and I would like to preserve the yard as much as possible so as to not agrivate the landlord. I also don't want my pup developing bad habbits for when I have my own yard. Both pups are on all natural foods, Chicken Soup for the Dog Lover's Soul Puppy Food and Call of the Wild so I am pretty sure they aren't deficient in any vitamins/minerals/etc.

Any help would be appreciated!

I'll bet she has some hound in her family tree somewhere along the line. Digging out animals they were bred to pursue and kill is a trait of some dogs. We had a beagle that dug a six inch hole in a new 800 dollar mattress.
All I can suggest is keeping her nails trimmed and maybe put some sort of booties on her when you find her digging. You don't have moles or voles in the yard.
Watch her in the house.
The Vet might have suggestions.