The quote from this article is illustrative of the issue.
"First, I thought [the cow] had died naturally, and then I got closer to it and I could see it wasn't natural," he said. "The eyes were gone, the tongue was gone. The ears were gone. The sex organs were cut out. It was just kind of weird."
The conventional explanation is that this matches what happens when cattle dies and lies in the field for a few days. Blood pools in the lower parts of the body, or is consumed by insects. Eyes, tongue, and other soft tissue are eaten by blowflies and vultures. "Precise" cuts appear due to bloating or dehydration.
No doubt this has been happening for as long as there have been cattle and ranchers chalked it up to cattle killed by predators. But in 1950s brought the UFO craze and now there was seemingly an explanation. Instead of looking for terrestrial explanations for odd occurrences, people began using extra-terrestrial ones. In the 1970s and 80s the UFO craze became increasingly exploited by books, television, and movies, some claiming to be documentaries, widening the public idea of a secret UFO invasion.
Aliens aren't the only ones blamed. Cultists, long associated with ritual animal mutilation, also get the blame. The media created in the public mind an idea of secret satanic cults surrounding sensational murderers like Ricky Kasso, Son Of Sam, the Zodiac Killer, and Charles Manson. Some are genuine cultists, some are not. Some might have mutilated cattle, but nobody has been caught in the act. But this added to the public imagination more explanations for mutilated cattle.
Cattle mutilation reached such a height in the US public consciousness that in 1974 the FBI was asked by the Senate to conduct an investigation citing numerous claims from ranchers of cattle mutilation. This investigation was completed in 1979 and concluded the cause was natural predators, plus some unexplained anomalies.
An alternative explanation is money. The aforementioned FBI report said 8,000 "mutilations" in Colorado cost ranchers an estimated million dollars. If this was due to natural causes, or the rancher's negligence, the ranchers are out. If this is due to a government cover up or cultists, maybe they can get compensated! It's not necessarily a sensible idea, but one can see the psychological lure: "it's not my fault, there's a government conspiracy"!