Q: Does Orthodox Communities Administer the Death Penalty?

According to the Mishnah (Sanhedrin 1:4) the death penalty could only be inflicted after trial by a Sanhedrin composed of 23 judges, we do not have a Sanhedrin in force at this time.  A court of 23 judges (Sanhedrin Ketannah) were considered competent to try capital cases.  The Sanhedrin Gedolah (the Great Sanhedrin) consisted of 71 members, was the Supreme Court of Appeal on all disputed points of law.  There were four types of death penalty (Sanhedrin 7:1): stoning, burning, slaying (by the sword), and strangling.
The death penalty is mentioned several times in Torah, however it was very rarely performed, less than once in every 70 years.  Our sages teach, "a court which puts a person to death once every seventy years is called a violent court." (Makkot 1:10).  Rabbi Akiva, a 1st century scholar, and Rabbi Tarfon, a 2nd century scholar, opposed capital punishment under all circumstances.  Also, the gravity with which members of the Sanhedrin viewed the responsibility of imposing the death penalty upon a criminal is evidenced by the fact that individual members fasted on the day on which they sentenced a person to death. (Sanhedrin 63a)
The Sages cite the verse in Shemot 21:15 to support their opposition to capital punishment.  Shemot 21:15 ends with the words mot yumat "that man shall surely be put to death."  Since the word for death is repeated in the Hebrew phrase (both mot and yumat are forms of the word for death), the Rabbis concluded that this was intended to teach that the death penalty is to be imposed only by G-d, not by man.  For, when the Bible wishes to indicate death at the hands of a human tribunal (as in Shemot 35:3), the word mot is used alone.
Just by the rules stated in Talmudic literature concerning the death penalty, the death penalty could hardly ever have been imposed.
Rabbi Isaac Herzog (1888-1959) in an article on the Sanhedrin published in 1932 states that the re-establishment of the Sanhedrin is dependent on the rebuilding of the Temple in the Messianic age, and that until the advent of Mashiach it is illegal to impose the death penalty for any offence, even for murder.  He did not know when he wrote this that the State of Yisrael would be established and that he would be its chief Rabbi.
With the establishment of the State of Yisrael, the Yisraeli Parliament, the Knesset, did debate whether or not to retain the death penalty as in the law established under the British mandate but the Knesset was not acting as a religious court or Sanhedrin, only as a secular body, although influenced in its decisions by Jewish religious tradition.  The debate between Rabbi Akiva, Rabbi Tarfon, and Rabban Simeon ben Gamaliel was referred to in the Knesset debate, and it was eventually decided to abolish capital punishment entirely except for treason committed in time of war.