Near the beginning, dogs are eating from a dead cow, and one is dragged into the carcass by the alien in a prolonged scene. It cries and whines, and then is pulled inside. It's around 9 minutes in.
Within the first few minutes of the film a cow gets sick and bloody and then dies of some sort of alien disease. Its carcass is then shown a few minutes later being eaten by dogs in a pretty graphic scene.
Later, when the main characters enter the town, a chicken has its head cut off. Not sure if it is an effect, or if it actually happened.