Sifrei Devarim Paragraph 151
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(דברים יז ז) יַד הָעֵדִים תִּהְיֶה בּוֹ בָרִאשֹׁנָה לַהֲמִיתוֹ – מִצְוָה בָּעֵדִים לַהֲמִיתוֹ.
(Devarim 17:7) "The hand of the witnesses shall be against him first to kill him": It is a mitzvah for the witnesses to kill him.
מִנַּיִן לֹא מֵת בְּיַד הָעֵדִים – יָמוּת בְּיַד כָּל אָדָם? תַּלְמוּד לוֹמַר: וְיַד כָּל הָעָם בָּאַחֲרֹנָה.
And whence is it derived that if he does not die by the hand of the witnesses anyone can put him to death? From "and the hand of all the people afterwards."
וּבִעַרְתָּ הָרָע מִקִּרְבֶּךָ – בַּעֵר עוֹשֵׂי הָרָעוֹת מִיִּשְׂרָאֵל!
"and you shall remove the evil from your midst': Remove the doers of evil from Israel.