The incident happened some time between 9pm on Saturday, February 11 and 8am on Tuesday, February 13.
The offender, or offenders, forced entry to the property in Rubery, West Midlands and, once inside, killed a calf.
A ewe was also dragged from an adjacent field and killed.
We’ve launched an investigation after three animals were killed during a break in at a property in Rubery t.co/9pGdiTcAxG— West Mercia Police (@WMerciaPolice)
It is believed they took the calf out of a shed with its mother and five other cows, slit its throat on the yard then dragged it to a open shed on site, butchered it and also brought a ewe to the shed from a neighbouring farm and butchered it.
A police spokesman said: "This was a sickening incident that would have undoubtedly caused a lot of suffering to the two animals. It is likely the animals have been killed for their meat.
"I’m keen to speak to anyone with information or CCTV, or who saw anything suspicious in the area. Please contact us, what may seem insignificant could fit into a bigger picture.
"If you have any information that could help our investigation, please call 101 quoting incident 130s of 13 February 2018.
"Also, information can be given anonymously through the independent charity Crimestoppers on 0800 555 111 or via www.crimestoppers-uk.org"