Question: Is an executioner who carries out the death sentence ordered by the judicial court guilty of killing in Buddhism?
Answer: Yes. As the Buddha ruled livelihoods that harm or kill sentient beings to be wrong, the executioner should quit instead of staying on to break the First Precept.
The idea of ‘just doing his job’ does not make sense if he can change his job. Even if an alternative Right Livelihood pays lower, he should still go for it, instead of staying on out of greed, while continually creating murderous negative karma.
In the eyes of Buddhism, legal killing is not always moral killing. Enlightened moral guidelines are not the same as unenlightened legal ones. Killing is an extreme response only for truly extreme situations, such as to save the lives of many others.
Question: Is the judge who ordered the death sentence according to the law to uphold order in society guilty of killing in Buddhism too?
Answer: Yes. The question itself is questionable, as most advanced countries have already abolished capital punishment because studies show that it does not substantially deter future crimes. In this sense, the death sentence does not truly uphold order in society. It can create chaos and distress instead, tearing families apart forever.
This is not to say there should be no ‘punishment’ at all, as there should still be appropriate incarceration for proper reformation. This is versus executing a person who might not be repentant, who might even be eventually reborn to continue disrupting society out of strong habitual forces. Likewise, the judge should consider changing his job, unless trying to reform the law.