The warning came after a 19-year-old man was arrested and charged in connection with illegal deer hunting with dogs on Knightswood Golf Course, as reported in the Evening Times on Thursday.
Officers raided two homes in Knightswood at about 9am. In one property, in Swallow Gardens, they found three skulls belonging to roe deer, an alligator head, two illegal snares and special hunting devices.
They also found an alaunt mastiff and a silica greyhound, which are well known hunting dogs.
The 19-year-old was charged under the Protection Of Wildlife Mammals Act and the Wildlife And Countryside Act.
A report will be sent to the Procurator Fiscal.
The dogs were not removed from the property because they showed no signs of ill-treatment.
Sergeant John Morrison, who is based in the pro- active policing unit at Stewart Street police office, has been leading the operation since March.
It culminated this week as part of Operation Myriad, a six-month surge of police activity based in A Division – covering the city centre and West End right out to Drumchapel – until the end of the month.
Two groups of six officers, as well as an inspector from animal charity the Scottish SPCA, were granted search warrants for the properties after an intense investigation into the killing of animals for entertainment.
Sergeant Morrison said in his 12 years of policing he had seen nothing like this.
He said: "To be honest, we didn't expect to find the skulls and everything else we found. The biggest thing we were expecting was the dogs.
"When you have in the police this long nothing usually shocks you, but we were all stunned by this.
"This was my first wildlife inquiry and it has been a steep learning curve for me."
This particular operation had started in May, but police have been investigating blood sports in green spaces across the city for years.
Sergeant Morrison said: "Deer have been hunted by gangs with dogs for years.
"These boys target areas such as Mugdock Country Park, the Bluebell Woods in Drumchapel, as well as Knightwood Golf Course.
"We hope our latest find will send out the right message and make people think before they take part in animal blood sport.
"We want the animals in the city, which are few and far between, to enjoy their local habitat and the public should be able to enjoy them without worrying about people carrying out blood sport.
"But these people are killing animals. It will not be tolerated by police and we will find the people behind it."
Sergeant Morrison called the latest result "significant".
The skulls and equipment, including head torches, lamps and a wooden bat designed to let dogs sink their teeth into after they have caught the animal, were found in a cupboard inside the home.
The reptile head was alongside them. It is believed it may have been imported from abroad.
Sergeant Morrison said: "We are still following inquiries into where the alligator head came from and what offences that may be connected to.
"We don't yet know how old the skulls are, but they are relevant to our inquiry."
The hunting snares are illegal because they do not have a device that stops the animal from being killed.
If an animal is caught in the snare, its throat is slit straight away.
Special collars used by hunters and designed to stop dogs from barking were also seized.
Sergeant Morrison said: "If you are on the golf course and the dog barks the animals can make an escape.
"So the collars spray lemon into the dog's nose to stop them from barking. It's a training device."
Scottish SPCA Chief Superintendent Mike Flynn said: "Deer and hare coursing is an abhorrent activity, where wild animals are chased and often mauled to death by dogs.
"Catching offenders is now a priority for the National Wildlife Crime Unit.
"We would welcome information from anyone, even anonymously, on 03000 999999 ."