The alleged attacks happened in the Inverkip area of Renfrewshire where two female roe deer were found with wounds officers believe to have been caused by a dog.
Both animals were likely pregnant with twins, according to police, and had to be humanly killed due to the severity of their injuries.
The grim discovery has prompted a warning from police to pet owners about the risks and dangers that out of control dogs can have on livestock and wildlife.
A police spokeswoman said: “With the arrival of spring it is timely to remind dog owners of their responsibilities when walking their dog in the countryside particularly on or around farmland.
"Lambing season has begun and roe deer will also be having fawns soon as well.
"Police Scotland have been made aware of two Incidents occurring recently in the Inverkip area whereby female roe deer have been found badly injured bearing wounds highly likely to have been caused by a dog attack."
The warning reminded pet owners that it is a criminal offence to allow dogs to chase, harass, injure or kill any wild animal or to worry livestock.
Those who commit the crime can face fines of up to £40,000 or 12 months imprisonment, according to the Protection of Livestock Scotland Bill.
She added: "The owner of the livestock or a person acting on their behalf can legally shoot a dog harassing or attacking sheep If the dog cannot be quickly brought under control.
"Dogs must be kept on close control and or on a lead at all times. If you are unable to call your dog back to you whenever required then you should simply not let your dog off the lead. Dogs are not ‘just being friendly, or wanting to play’ when they chase sheep or deer they are blindly following their instinct to hunt and kill, even if they are unskilled at doing so.
"Please be responsible and do not let your dog run off lead out of control.”