Rabbis assert that they dispensed justice in Sanhedrin while the Temple stood. It would be odd if the rabbinical Sanhedrin sat in the Temple, which was controlled by Sadducees who derided all the rabbinical concepts.
After the bar Kochba revolt, Jews lost jurisdiction over criminal matters. By some accounts, Jerusalemites lacked the power of capital punishment still a century earlier, when Roman procurators had to approve executions. Under Roman law, religious violations were not subject to capital punishment. Exceptions were rarely made for whatever religion currently happened to be official in Rome. For our purposes, it matters that at least after Herod the Great Jews were unable to exercise caret, capital punishment for the numerous (thirty-eight) religious transgressions set out by the Torah. Nor were Jews able to exercise capital punishment for other religious crimes, crimes for which the Torah prescribes specifically death rather than caret (removing the transgressor’s soul from among his people).

Rabbis, accordingly, made face-saving changes to Jewish law. They made death sentences impractical by erecting impossible standards of proof. And they placed authority for capital punishment in the hands of the Sanhedrin, which was hardly operational, certainly not as a criminal court, after 135 CE. Executions therefore were made legally impossible, though they were seemingly carried out against Jewish traitors who endangered their communities before gentiles.

Rabbis also redefined caret as afterlife punishment. Initially it was understood as non-resurrection. That raised a practical problem: once a sinner was assured of damnation, he had no reason to mend his ways. Caret, accordingly, was reinterpreted as series of increasing difficulties in communication with God. A similar process underlies the evolution of the rabbinical doctrine of Hell. Initially a place of eternal tortures (Josephus, War 2:8:14), Hell became a purgatory with varying terms of sentence.

Historically, rabbis did disburse capital punishment in the absence of the Sanhedrin. The rabbinical doctrine that malshin, Jewish informants, were liable for execution because they endangered entire communities, could only have developed with capital jurisdiction in mind. Even Christian rulers, eager to avoid pogrom violence, granted Jews the authority of capital punishment in regard to informers, such as in Barcelona in 1383. In Thessaloniki, capital crime jurisdiction was granted by Christians in 1558 and confirmed by the invading Muslims. A famous case of execution of informants took place in the Ukrainian town of Ushitza in 1836. Jews in other countries too, executed traitors.

Today, rabbis use the absence of Sanhedrin as an excuse to avoid punishments for religious transgressions, including executions of Jewish traitors who seek to abandon the Land of Israel.