According to WLOS, Shariah Jessamyn Metzger, 26, and Jace Lee Greene, 29, are accused of mutilating the cat, posting pictures of the body online, and then leaving it on the property of the Ingles grocery store at 669 Haywood Road.
Police are still searching for Zackery Eugene Greene in connection with the incident.
Metzger and Greene have been charged with the improper burial of an animal.
Veronica Coit of "Asheville Cat Weirdos" said she saw pictures of a cat's body on Instagram and called the police.
"To think of what these monsters did to a cat that was sweet and friendly is awful," she told WLOS.
Kitty, the 2-year-old cat who was killed, belonged to Aaron Naster.
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Naster said Kitty was sweet, trusting, and loved people.
A necropsy will be performed on the cat this week to determine its cause of death.
Both are being held under a $15,000 bond.