My guess is rabbits. Look at the branch and if the cuts are at about 45 degrees angle then it is Peter Cotton Tail. Leave your dog outside, that will keep the critter/s away.

Thanks for the response! My puppy is still a baby though. Only 10 weeks old! I can't leave her outside by herself yet. She's small enough still to fit through the gate. Any other ideas?

Squirrels do not eat these plants, but both rabbits and deer will. The tooth marks of both the rabits and deer will be similar. The most effective means of control I have found is a good, tight fence that will prevent those buggers from getting near anough to eat the vegetation.

Ellyni,
Deer tooth cuts are straight across the stem not at an angle like rabbits. There are commercial sprays which DETTER rabbits. The most effective products contain something that smells bad and something that tastes bad to the varmint. Make sure you read the entire label before purchasing and before applying.

A good product to use would be capsaicin oil, it comes from peppers and it is hot to those plant chewers. Typically rabbits/squirrels don't like the oil, some may still find it tasty, but it is worth a shot. It won't harm your puppy or the rabbit/squirrel it is just hot enough to keep them away. Usually nurseries carry some.