The justices voted 5-4 Wednesday to deny the petition. The execution is scheduled Wednesday evening at the State Penitentiary in Parchman.
The attorney general's office argued that Gary Carl Simmons Jr. provided no new evidence to support cancelling the execution.
Simmons' lawyers said his previous legal team didn't pursue medical examinations of Simmons that would have revealed mental health issues. They said Simmons should be allowed to pursue those claims.
Simmons, now 49, is scheduled to be executed for the 1996 killing of Jeffery Wolfe, whose body was found in pieces in a Jackson County bayou. Simmons also was convicted of kidnapping and raping Wolfe's friend and sentenced to life on those charges.
If the execution happens, it will be the sixth in Mississippi this year, the most here in a single year since eight in 1956.
Simmons and his former brother-in-law, Timothy Milano, were both convicted of killing Wolfe. Milano was sentenced to life.
Authorities say Milano shot Wolfe, but Simmons planned the killing, dismembered Wolfe and raped Wolfe's friend.
Court records say that Simmons planned the death and dismemberment of a drug dealer because he didn't have the money to pay him for marijuana.
Wolfe and his female friend went to Simmons' house in Jackson County on Aug. 12, 1996, to collect the debt — estimated at as much as $20,000. Milano shot Wolfe numerous times with a .22 caliber rifle inside Simmons' home, according to court records.
Simmons raped the woman and put her in a metal box and used bolt cutters and the knives from his grocery store butcher job to dismember Wolfe in the bathtub, the court records said.
The woman escaped the next day and pieces of Wolfe's body were found in a bayou behind Simmons' home.
Simmons lawyers said in a motion Tuesday that recent mental exams show he has long-term substance abuse problems, post-traumatic stress disorder and "mild executive-level brain dysfunction." They also argue that his previous lawyers didn't do a good job.
The attorney general's office has argued in the past that Simmons' sanity "is not in question."
Simmons' current attorneys say his trial lawyers didn't explore mental health problems for sentencing purposes and the issue wasn't properly raised by previous appeal lawyers.
Simmons' previous appeals have been rejected by Mississippi courts and the U.S. Supreme Court.