Any living critter in Ark has the posibility of dropping raw meat when harvested. Even a dead player can be harvested for raw meat, and there is no distinction between meat harvested from animals or humans. It's all just raw meat.
For the most part, the larger the animal the better the chances for raw meat - and the more likely you are to get larger quantities. Dodos are an easy early food source for raw meat, while the Phiomia is a virtual raw meat pinata; the only problem is that it's one of the fastest running land Dinos I've seen so far.
One thing to keep in mind is that if your Dino kills something it may harvest the meat. Herbivores simply don't, but a carnivore can and often will. Simply access the Dino's inventory to see if it has picked up any goodies.
Now the harvesting of animals once they are dead is rather interesting. In fact, for a premier survival game it's quite weird, but there are no proper tools for this task. When you harvest an animal it seems to balance out like this. A Pick, metal is better than stone, and it may yield more meat and less hides. Using a Hatchet, metal is better than stone, will tend to yield more hides and potentially less meat.