Under Arizona law, the jury had to determine whether Arias had been "exceptionally cruel" when she shot and killed Alexander.
"He was stabbed in the heart, chased down and then he had his throat slit," Prosecutor Juan Martinez said. "Those approximately two minutes that we talked about must have seemed like two lifetimes."
The news comes just a week after Arias was found guilty of first-degree murder for shooting, stabbing and almost decapitating Alexander. She told reporters that she would prefer the death penalty to life in prison.
"The worst outcome for me would be natural life [in prison]. I would much rather die sooner rather than later," she said.
"I said years ago I'd rather get death than life. I believe death is the ultimate freedom."
Arias' defense attorney, Kirk Nurmi, asked the jury to consider whether her actions went "beyond (the) normal cruelty that's inherent in any first-degree murder."