According to the Mishnah (Sanhedrin 1:4) the death penalty could only be inflicted, after trial, by a court composed of twenty-three judges and there were four types of death penalties (Sanhedrin 7:1): stoning, burning, slaying (by the sword), and strangling. A bare reading of these and the other accounts in the tractate would seem to suggest a vast proliferation of the death penalty. Yet, throughout the Talmudic literature, this whole subject is viewed with unease, so much so that according to the rules stated in that literature the death penalty could hardly ever have been imposed...
...the right to impose the death penalty had been taken away from the Jewish courts by the Roman authorities. According to one report in the Talmud (Sanhedrin 41a) the power of the Jewish courts to the death penalty ceased around the year 30 BCE; according to another report (Sanhedrin 52b) it could only have been imposed while the Temple stood and must have come to an end not later than 70 CE when the Temple was destroyed.
The first opinion was saying that the Jewish court had the power to rule death penalties only if they were in their proper location, the Beis Hamikdash, see this note by the Soncino Talmud on Sanhedrin 41a.
"Deut. XVII, 10: And thou shalt do according to the tenor of the sentence which they shall declare unto thee, from that place; this implies that it is the place that conditions the authority of the Sanhedrin in respect of the death sentence. [J. Sanh. I, 1 has, 'the right to try capital cases was taken away from them, i.e., by the Romans. For a full discussion of the subject v. Juster. op. cit, II, 138ff.]"
The second opinion is saying that the power to rule death penalties comes from the Beis Hamikdash, once that was destroyed, regardless of where the court was, the power to give death penalties ceased.
It is important to note that death penalties were occurred very rarely throughout Jewish history.
As the myjewishlearning.com article continues
(Mishnah Makkot 1:10): "A Sanhedrin that puts a man to death once in seven years is called destructive. Rabbi Eliezer ben Azariah says: even once in seventy years.