He wants her out of the room. She hasn't see death. Of course she has seen the aftermath though. He has seen death; he has watched people die, at his own hand even.
It changes you to see someone die. He didn't want his Bones to go through that. He didn't want her to see the life leave someone's body, even if it was at that person's own hand. If that was even the intention, he could be trying to hurt either one of them.
"Bones, leave," Booth pleaded. To his surprise she left right away. Good, one crisis averted, he thought as she left. He didn't want her to see life leaving someone's body, something that would add on to her nightmares. But he didn't want her hurt, if it came down to that.
With her out of the room and safe Special Agent Seely Booth was able to fully concentrate on the task at hand. Stopping Jack Cuttler from killing himself.