The society is offering a $US3000 reward for information leading to the arrest and conviction of those responsible for the killing, which occurred in West Valley, near Salt Lake City.
American Dog Rescue, based in Salt Lake City, is similarly offering a $US2500 over the killing.
Snap's body was found by his owner, Jennifer Carrillo, on Wednesday evening. Snap had been shot and mutilated in the pasture where Carrillo grazes several horses.
Sergeant Zach Todd, of Salt Lake County Animal Services, went to the scene at 5600 West and California Avenue with officers of the Salt Lake City Police Department.
Snap appeared to have at least one gunshot wound, according to Todd.
The portions of Snap's body that were cut off are consistent with areas that would be removed for consumption and the butchering appeared to be professionally done, according to a crime scene technician called to gather evidence.
Bloodstains were found stretching out about 100 square feet around Snap's body.
"It does not appear that the horse immediately went down," Todd said. "It is not acceptable to kill a horse in this manner and we are dedicating the resources necessary to investigate this case."
Arthur Benjamin, a Salt Lake County Animal Services supporter and founder of American Dog Rescue, has provided the county with resources to help with the investigation.
In addition to the $US2500 reward, Benjamin is sponsoring a necropsy to determine Snap's cause of death.
"There is no doubt that this majestic animal suffered before he was brutally slaughtered," Benjamin said. "Snap was someone's beloved companion and he deserves justice."
The Humane Society of Utah's executive director, Gene Baierschmidt, echoed the sentiment. "We think this was a cruel and callous act, especially if the horse was still alive when it was dismembered.
"In the more than 20 years I've been at the Humane Society of Utah, this has been one of the most egregious acts of cruelty I've heard of.
"We hope the reward will encourage anyone with knowledge of this incident to come forward and provide information that will lead to the arrest and conviction of the perpetrators of this crime."
Under Utah's animal cruelty code, the killing is considered a Class A misdemeanor which carries a sentence of up to a year in prison and a fine of $US2500.
The owner of the horse may also take civil action against those found guilty of committing this crime.