That certainly doesn't sound like an endorsement of the death penalty.
Shira and BRTD
The woman in question was accused of adultery. No where in the US is the death penalty imposed for adultery. In the biblical story Richius cited the woman was not punished at all. In most cases of adultery in the US, the adulterer would not be punished either, and certainly would not be stoned to death.
But what about murder and other violent crimes? I don't know what Jesus would say, but in my opinion the death penalty is a just and fitting punishment for certain crimes. I've given examples of such crimes in other posts but let me cite two of them again and ask what punishment you think is fitting.
A man raped a 16 year old girl and then cut off her arms. In this case there was no murder so the death penalty would not be imposed in any state in the country, but I think it should be. Imagine being that poor young woman. Imagine trying to feed yourself, or bathe, or dress yourself or use the bathroom by yourself without arms. Imagine looking in the mirror and seeing stumps where your arms once were, and being reminded every day of the horrible crime that was committed against you. Imagine never being able to touch those you love with your fingers. What do you think should be the punishment for such a horrible crime?
In another case someone carjacked a young woman and her children. He raped and murdered her and then drowned her children one at a time in a nearby stream. Imagine the terror and pain the victims felt. Imagine the anguish of the father who lost his entire family to this brutal animal. Then tell me what should be the appropriate punishment.