Jasper was executed with a lethal dose of pentobarbital Wednesday evening in Huntsville, Texas, the San Antonio Express-News reported.
He was convicted and sentenced to death in 2000 for the 1998 slaying of Alejandro. Two other men convicted in the case -- Steve Russell and Douglas Williams -- were both sentenced to life in prison.
Authorities said Jasper intended to rob Alejandro of recording equipment during a recording session at the victim's home. Jasper admitted to using a kitchen knife to cut the Alejandro's throat.
However, Jasper has maintained that he wasn't responsible for Alejandro's death, alleging that 25 stab wounds inflicted by Williams and Russell were the victim's actual cause of death.
"I'm on death row and yet I didn't commit the act of murder," Jasper said in a seven-page letter he recently sent to Gawker.com.
No one from Jasper's family attended the execution. Neither did anyone from Alejandro's family, who oppose the death penalty.