Which predators only eat some parts of their prey? (Warning — graphic content)
In the pictures shown above only the soft part of the animals have been eaten. This is common for most predators as these are the easiest parts to eat.

Correct me if I am wrong but the animals seem to not have severe bite marks around the neck. This means the predator was not big. You can pretty much rule out anything around the same size or bigger than the sheep.

To exactly identify what killed them just from a carcass is hard, and even harder over the internet. However, it looks like you are dealing with feral dogs, coyotes or wolves, although with wolves and dogs there would generally be more scarring around the neck of the sheep.

Dogs: I have seen this behavior in dogs. These are normal tame dogs that have discovered the kick of hunting. Where I come form in South Africa the farmers tend to shoot dog packs if they see them on their land. This is because it is a common problem for the packs to attack chickens, sheep or even calves.  They get an immense kick from hunting the sheep but in most cases don't eat it, not like the photos shown at least.

Foxes: Although it may be hard to believe foxes have also been known to kill sheep. However, in your case it is not likely to be foxes. Foxes hunt alone and tend to kill lambs.

Coyotes: Coyote packs have almost identical behavior to dog packs. The difference being that they pick one sheep and kill it quickly. They do not do it 'for the kick' like dogs and rather for the food. Judging from the photos I would say it is possible that this was done by wild Coyotes, if they are found in your area. Coyotes are also not very shy, and will often hunt close to where people live.

Wolves: While possible, I would rule out wolves because of your geographical location. Wolves also tend to be more shy and will stay away from places with lots of people, like a city.

Source:
http://www.omafra.gov.on.ca/english/livestock/sheep/facts/02-029.htm