I would like to know from Torath Mosheh Jews: Since Torath Mosheh Jews are so adherent to the Torah, do you still follow the edicts of capital punishment found in the Torah such as stoning, etc.?
According to Torath Mosheh, capital punishment is only something that is carried out when there is a Torah based nation in the land of Israel. Of course there has been no such situation for ~2,200 to 2,300 years.
It is something that only can only be done at the judgement of the Torah based Supreme Court called the Beith Din HaGadol or Sanhedrin. Further, the laws set in place by both the written Torah (in Hebrew) and the oral Torah are so stringent on the burdon of proof for performing such an act that it would take a LOT for a Jew/Israel to be executed.
Literally, the person would have to stand up in front of the Torah based Supreme Court and make an Emperor Palpatine like speach about how they did, they understand what they were doing when they did it, they have their own witnesses that said they did it, the witnesses warned them about what they were doing and the consquences, and that they are doing so publically in order to lead the Israeli nation astray. That is the level it would take.
Further, if you look back in Jewish history very few executions ever took place - except for in some very extreme situations similar to what was mentioned above.