Jerusalem Talmud Sanhedrin 7.3

משנה: מִצְוַת הַנֶּהֱרָגִין. הָיוּ מַתִּיזִין אֶת רֹאשׁוֹ בַּסַּיִיף כְּדֶרֶךְ שֶׁהַמַּלְכוּת עוֹשָׂה. רִבִּי יְהוּדָה אוֹמֵר נִיוּוּל הוּא זֶה אֶלָּא מַנִּיחַ אֶת רֹאשׁוֹ עַל הַסַּדָּן וְקוֹצֵץ בַּקּוֹפִיץ. אָמְרוּ לוֹ אֵין מִיתָה מְנוּוֶּלֶת מִזּוֹ.

MISHNAH: The order of beheading. They were chopping off his head with a sword just as the [Roman] government does. Rebbi Jehudah says, this is ugliness but one puts his head on the block and cuts it with a butcher knife. They told him, there is no death uglier than this.

הלכה: מִצְוַת הַנֶּהֱרָגִין כול׳. מוֹדֶה רִבִּי יְהוּדָה שֶׁאֵין מִיתָה מְנוּוֶּלֶת מִזּוֹ. אֶלָּא שֶׁאָמְרָה תוֹרָה וּבְחֻקּוֹתֵיהֶם לֹא תֵלֵכוּ. אָמַר רִבִּי יוֹחָנָן. וְתַנֵּי כֵן. יִרְצַח הָרוֹצֵחַ. בְּמַה שֶׁרָצַח. יָכוֹל אִם הֲרָגוֹ בְסַיִיף יַהַרְגֶּנּוּ בְסַיִיף. בַּמַּקֵּל יַהַרְגֶּנּוּ בַּמַּקֵּל. נֶאֱמַר כָּאן נְקִימָה וְנֶאֱמַר לְהַלָּן וְהֵבֵאתִי עֲלֵיכֶם חֶרֶב נֹקֶמֶת נְקַם בְּרִית. מַה נְקִימָה שֶׁנֶּאֶמְרָה לְהַלָּן בְּחֶרֶב. אַף נְקִימָה שֶׁנֶּאֶמְרָה כָאן מִיתָה בַּחֶרֶב. יָכוֹל יִטְלֶינּוּ מִבֵּין הָאַגַּפַּיִים. נֶאֱמַר כָּאן וּבִעַרְתָּ הָרָע מִקִּרְבֶּךָ. וְנֶאֱמַר לְהַלָּן וְאַתָּה תְּבַעֵר הַדָּם הַנָּקִי מִקִּרְבֶּךָ. הַבְעָרָה הַבְעָרָה. עֲרִיפָה עֲרִיפָה. מָה הַבְעָרָה שֶׁנֶּאֱמְרָה לְהַלָּן מוּל הָעוֹרֶף אַף כָּאן מוּל הָעוֹרֶף. מָה עֲרִיפָה שֶׁנֶּאֱמְרָה לְהַלָּן הַתָּזַת הָרֹאשׁ אַף כָּאן הַתָּזַת הָרֹאשׁ.

HALAKHAH: “The order of beheading,” etc. “Rebbi Jehudah agrees that there is no death uglier than this but the Torah said, in their statutes you shall not walk.” Rebbi Joḥanan said, also it was stated thus: One shall murder the murderer, the way he murdered. I could think that if he killed with a sword, one should kill him with a sword, with a rod one should kill him with a rod? Avenging is written here, and there it is written: I shall bring over you a sword which avenges the vengeance of the Covenant. Since avenging mentioned there is by the sword, also avenging mentioned here is by the sword. I could think that he should kill him between the arms? It is said here, you shall eliminate the evil from your midst, and it is said there, you shall eliminate the innocent blood from your midst. Elimination, elimination; breaking the neck, breaking the neck. Since elimination here is at the neck, also there it is at the neck. Since breaking the neck there implies chopping off the head, also here chopping off the head.