Staff at Forge Mill Farm in West Bromwich are appealing for help to catch the culprits behind the theft which took place on the night of October 24.
This comes after two rare breed lambs were stolen from the farm earlier this year and multiple reports of thefts from Sandwell Valley Country Park nearby.
Councillor Danny Millard is the cabinet member for culture and tourism at Sandwell Council, which runs the farm.
He said: “This is a callous, inhumane and criminal act, having a farm that is accessible to all our residents provides a real benefit to the all parts of our community.
"This kind of selfish behaviour will not be tolerated and I urge anyone that has information to contact the police.”
There has been a spate of sheep rustling incidents in Sandwell Valley Country Park since April which have left staff devastated. It means there will be around 10 to 20 per cent fewer lambs on show for visitors at Forge Mill next spring.
Alex Dunn, farm manager at Forge Mill farm said: "This is a devastating loss to the farm and to the people of Sandwell, after all these are their sheep, we are here to serve the public and to provide experiences and educate about food and farming.
"It is heart-breaking to think that some of the same people we serve might also be responsible for stealing and slaughtering these sheep in such an inhumane manner.
"Please help us catch those involved so we can continue to keep sheep at Sandwell Valley for everybody to enjoy."
Farmers and staff are concerned for the welfare of the remaining sheep and fear that the stolen ewes may have lost or will lose their lambs due to the stress of the incident.
Extra security staff have now been hired and new CCTV cameras are being installed at the farm next to Sandwell Valley, while new technology to help track the animals is being investigated.
The council said there had also been a separate related incident in Smethwick over the weekend.
Any members of the public with any information should call 101 and quote the crime number 20/183 0794/21.