Does Talmud introduce death penalties not mentioned in the Torah?

Question

Does the Mishna or Gemara introduce any sin as liable for the death penalty, not mentioned in the Torah?

Answer 1

Our Sages in the Talmud introduced two types of such penalties:

1. Threatening with Heavenly punishment on behalf of Heavenly court (see Danny's example). To enforce their Rabbinical decrees over which they had little control, they accompany many of them by invoking Heavenly capital punishment. In other words, "those who will not obey our decrees will be severely punished by G-d". (I don't know exactly the mechanism of how this works if anything, but it is surely a good educational measure.)

2. While not mentioned explicitly anywhere in the writings, the Sages proclaimed the authority to execute any punishment they see fit, including corporal and capital, for any misdeed - Biblical or Rabbinical in every specific case. In other words, the Talmud allowed the Rabbis to override the Biblical punishment (lashes) and execute a person if they see a special need, not sanctioned by the Torah. See Sanhedrin 46a with explanations:

   תניא ר"א בן יעקב אומר שמעתי שבית דין מכין ועונשין שלא מן התורה ולא לעבור על דברי תורה אלא כדי לעשות סייג לתורה ומעשה באחד שרכב על סוס בשבת בימי יונים והביאוהו לבית דין וסקלוהו לא מפני שראוי לכך אלא שהשעה צריכה לכך שוב מעשה באדם אחד שהטיח את אשתו תחת התאנה והביאוהו לבית דין והלקוהו לא מפני שראוי לכך אלא שהשעה צריכה לכך:

   It is taught in a baraita: Rabbi Eliezer ben Ya’akov says: I heard that the court may administer lashes and capital punishment, even when not required by Torah law. [And they may not administer these punishments with the intention of violating the statement of the Torah, i.e., to disregard the punishment stated in the Torah and administer another punishment; rather, they may administer these punishments to erect a fence around the Torah, so that people will fear to sin.]

   And an incident occurred involving one who rode a horse on Shabbat during the days of the Greeks, and they brought him to court and stoned him, not because he deserved that punishment, [as riding a horse on Shabbat is forbidden only by rabbinic decree,] but because the hour required it, [as people had become lax in their observance of Shabbat and therefore it became necessary to impose the severe punishment for a relatively minor offense].

   Another incident occurred involving a man who engaged in intercourse with his wife in public under a fig tree, and they brought him to court and flogged him, not because that punishment was fitting for him, as such conduct is not forbidden by the Torah, but because the hour required it. [People had become remiss in matters of modesty; therefore, stringent measures had to be taken to rectify the situation.]

Answer 2

Yes. See the Chochmas Adam in Klal 152 who says:

1. One who doesn't tear Kriah for his 6 close relatives - even though it's a Rabbinical Mitzvah - is liable for the death penalty by Heaven.

2. Anybody who transgresses a Rabbinical Mitzvah is liable, implying liable for the Heavenly Death Sentence.

מי שיש לו מת שהוא קרובו והוא מהמתים שראוי להתאבל עליהם והם אביו ואמו ובנו ובתו ואחיו ואחותו בין מצד אביו בין מצד אמו ואשתו חייב לקרוע מדרבנן ועונשו מיתה בידי שמים אם אינו קורע ואסמכוה אקרא דכתיב גבי בני אהרן ראשיכם אל תפרעו ובגדיכם לא תפרומו ולא תמותו ודרשינן אתם לא תמותו הא אחר שלא פרע ושלא פרם חייב מדרבנן כמו שאמרו במקום אחר כל העובר על דברי חכמים חייב