The animals were killed within a few days of each other, either with their heads twisted backwards or their throats cut.
The horned goat is a symbol in the occult, intended to mock the image of Jesus as the 'lamb' who died for Man's sins, after a reference in the Bible to the obedient sheep being separated from the unruly, non-believing goats.
© swns.comWorried: Jimmy Small, 66, pictured with his last remaining goat
Retired farmer Jimmy Small, 66, who lost two of his goats to the killer in Tipton St John, Devon, said: 'The whole village is up in arms over what is happening.
'Everyone is talking about it and locals are keeping their eyes open. I recognise it could have something to do with the occult. What sort of people could do this?'
Mr Small lives alone and had kept his goats, Blacky and Anita, as pets for about seven years.
He said: 'I found Blacky dead first with his neck twisted back, just before Easter. Then two days later Anita was lying dead in exactly the same spot.
'It has to be some kind of ritual, otherwise it is too much of a coincidence. Who could kill a defenceless animal? Mine were really roughed up, they had definitely been kicked about.
© Google StreetviewSlaughterings: Four gotats have been killed in Tipton St John
Mr Small has lived in Tipton St John all his life and said he had never seen anything like this before. The other killings happened at a smallholding 300 yards away.
The owner, who wished to remain anonymous, said: 'I found two of my goats dead within 48 hours of each other.
'When I told my vet he advised me to read a book on the occult. He seems to think the way the goats were killed and because they were horned, it may have something to do with satanic ritual.
'The first animal I lost was Gremlin, who I found with his head twisted back.
'At first I thought it was a bizarre accident. The next involved the mother goat, Gladys. We found her the day after Easter Monday with her throat cut from ear to ear.
'The body had been dragged to the same spot where the other goat was found. I have had to move my remaining goat, Goblin, to a secret location after the death of its mother and brother.
'I'm devastated. They were so adorable, children used to come and pet them, but since it happened I go to bed every night thinking about them.
'It's a satanic thing, I'm sure of it. All this is spoiling our lives.'
Devon and Cornwall Police confirmed they were investigating the killings.
© AlamyThe village of Tipton St John, overlooking the vale of the River Otter, is scene of the goat killings
The people in this rural British area can deal with this well. They just need to organize a bit and confront those who move about by night, perhaps up to no good. But oh no, it's all up to the absent authorities!
This sort of thing wouldn't go on very long in the US. Even in most of the urban and suburban areas in the US - except for New York City and Chicago - two out three households are armed. In the rural areas like this one in the UK, it's 100 per cent, even if it is just a .22 rifle for use against pests.
The satanist yobs might cool it if one or two caught a bullet and died.