The juror, who was working at night to keep up on his job, was caught napping by the judge and other courtroom observers Thursday.
The judge dismissed the juror and replaced him with an alternate who listened to defense experts who hope to spare Joshua Stepp's life.
Stepp admitted to killing his stepdaughter in a rage. His defense team has told jurors the rage was the direct result of posttraumatic stress disorder from his combat service in Iraq.
A psychiatrist hired by the defense testified Thursday morning that Stepp had many gory experiences in Iraq including having to pick up body parts of an acquaintance killed by a suicide bomber.
"These are all cumulative things that over time he said he didn't feel like himself anymore," forensic psychiatrist Dr. Nicole Wolfe said.
Stepp was living with his new wife, his toddler daughter from a prior marriage and his wife's infant daughter from a prior relationship back in November 2009 at their south Raleigh apartment complex.
The baby, 10-month-old Cheyenne Yarley, was beaten to death and investigators believe sexually assaulted.
Stepp denied the sexual assault, but while on the stand he told jurors he was unnerved by the baby's constant crying, lost it and shoved Cheyenne's head into the carpet killing her.
"In my opinion Mr. Stepp also had posttraumatic stress disorder which would have been a factor on this particular day," Wolfe said.
But on cross examination a prosecutor grilled Wolfe about her findings.
"Were his cognitive or thinking abilities significantly affected by these disorders," prosecutor Adam Moyers asked.
"No," Wolfe replied.
If jurors find Stepp guilty of first-degree murder, they will then have to decide whether he gets the death penalty.