The 3-year-old girl and her mother, who was also in the room during the struggle between 49-year-old Ronald Marquez and officers, were hospitalized, police said.
The relative who called police said an exorcism had also been attempted Thursday.
"The purpose was to release demons from this very young child," said Sgt. Joel Tranter.
Officers arrived at the house Saturday and entered when they heard screaming coming from a bedroom, Tranter said.
A bed had been pushed up against the door; the officers pushed it open a few inches and saw Marquez choking his bloodied granddaughter, who was crying in pain and gasping, Tranter said.
A bloody, naked 19-year-old woman who police later determined to be Marquez's daughter and the girl's mother was in the room, chanting "something that was religious in nature," Tranter said.
The officers forced open the door enough for one to enter, leading to a struggle in which an officer used a stun gun on Marquez, Tranter said.
After the initial stun had no visible effect, another officer squeezed into the room and stunned him. The girl was freed and passed through the door to the relative, Tranter said.
Stun guns are electrical self-defense weapons. Touching a person with the prongs of the stun gun quickly immobilizes the attacker. However, because stun guns have very low amperage, no serious or permanent injury is inflicted.
Marquez was placed in handcuffs after a struggle with officers and initially appeared normal, but then stopped breathing, Tranter said. He could not be revived and was pronounced dead at a hospital.
The cause of death was not immediately known, and autopsy results probably will not be available for several weeks, Tranter said.
The mother was not arrested, but police will consider criminal charges, Tranter said.