The victim, a 16-year old student of standard seven of a school for the blind here, was found by her mother lying in a pool of blood at the back of her house at Puhundi village, the police said.
She was rushed to the Patrapur community health centre which referred her to MKCG Medical College and Hospital here.
Her condition is critical and she is not in a position to speak as her vocal chord had been affected in the attack, doctors attending on her said.
The girl's father and another brother work outside the state, police said.
Additional superintendent of police of Berhampur, Trinath Patel along with the scientific police team and sniffer dog squad rushed to the spot for investigation.
"Though the miscreants tried to kill the visually challenged girl by slitting her throat, the alleged rape attempt will be known only after medical examination," Patel said.