Ramban on Deuteronomy 19:13

לֹא תָחוֹס עֵינְךָ עָלָיו, שֶׁלֹּא תֹאמַר הָרִאשׁוֹן כְּבָר נֶהֱרַג לָמָּה אָנוּ הוֹרְגִין אֶת זֶה וְנִמְצְאוּ שְׁנַיִם הֲרוּגִין, לְשׁוֹן רַשִׁ"י (רש"י על דברים י"ט:י"ג) מִסִּפְרֵי (שופטים קפז). וְהַטַּעַם שֶׁלֹּא תֹאמַר, כַּאֲשֶׁר נָחוּס עַל דַּם הֶהָרוּג טוֹב שֶׁנָּחוּס עַל דַּם הַחַי. וְהַנָּכוֹן כִּי הַכָּתוּב יְצַוֶּה בְּחַיָּבֵי הַמִּיתוֹת וּבִעַרְתָּ הָרָע מִקִּרְבֶּךָ, וְהִיא מִצְוַת עֲשֵׂה, אֲבָל בִּמְרֻבֵּי הַתַּקָּלוֹת יַזְהִיר עוֹד בְּמִצְוַת לֹא תַעֲשֶׂה שֶׁלֹּא יִנָּצְלוּ מִיָּדֵנוּ, לֹא מִפְּנֵי מוֹרָאָם וְלֹא שֶׁנִּתֵּן לָהֶם רַחֲמִים. וְכָךְ הִזְכִּיר בַּמֵּסִית (דברים י"ג:ט'), וְאָמַר מְכַשֵּׁפָה לֹא תְחַיֶּה (שמות כב יז), מִפְּנֵי הֱיוֹתָהּ רַבַּת הַמְּהוּמָה הַמּוֹכֶרֶת רַבִּים בִּכְשָׁפֶיהָ; וְקַצֹּתָה אֶת כַּפָּהּ לֹא תָחוֹס עֵינֶךָ (דברים כ"ה:י"ב), מִפְּנֵי כִּי הַפְּתָאִים יְהַלְלוּ אוֹתָהּ בִּהְיוֹתָהּ עוֹזֶרֶת לְבַעְלָהּ, אוֹ מִפְּנֵי שֶׁהַבֹּשֶׁת מָצוּי וְאֵין בּוֹ חֶסְרוֹן כִּיס; וְכֵן בְּעֵדִים זוֹמְמִין צִוָּה (דברים י"ט:כ"א) שֶׁלֹּא יְרַחֲמוּ עֲלֵיהֶם, בַּעֲבוּר שֶׁלֹּא נַעֲשָׂה בְּעֵדוּתָם דָּבָר, אוֹ מִפְּנֵי שֶׁתַּקָּלָתָם מְרֻבָּה: THINE EYE SHALT NOT PITY HIM. “This means that you shall not say, ‘The first person has already been killed. Why should we kill him also, with the result that two people will be killed?’” This is Rashi’s language quoting the Sifre.²⁶⁵Sifre, Shoftim 187. The meaning thereof is that you should not say, “Rather than having pity on the blood of the slain it would be better to have pity on the blood of the living one.”
The correct interpretation of the verse is as follows: Scripture has commanded concerning those liable to death, so thou shalt put away the evil from the midst of thee,²⁶⁶Above, 17:7. this being a positive commandment. But in matters of prevalent danger [to society], He warned further with a negative commandment that [the murderers] not be spared from [punishment at] our hands, neither on account of fear of them nor because we might show them mercy. He mentioned the same in the case of the inciter.²⁶⁷Ibid., 13:9. He also stated, Thou shalt not suffer a sorceress to live²⁶⁸Exodus 22:17. because of her being full of tumult²⁶⁹Ezekiel 22:5. who sells many through her sorceries.²⁷⁰See Nahum 3:4: that selleth nations through her harlotries. And thou shalt cut off her hand, thine eye shall have no pity²⁷¹Further, 25:12. — this was commanded because the fools praise her for having been a help to her husband [who was fighting with another man], or because embarrassment is common and involves no monetary loss [and therefore the Torah was strict in the punishment thereof]. Similarly in the case of plotting witnesses He commanded that we have no pity on them,²⁷²See Verse 21. [thinking that] because nothing had yet been done to the accused²⁷³See Ramban on Verse 19. [therefore we should not punish them], or perhaps [the strictness is] due to the prevalence of their danger.

וְטַעַם וְטוֹב לָךְ, כִּי בִּעוּר הַדָּם הַנָּקִי מִצְוָה וְטוֹבָה גְּדוֹלָה לְךָ לְהַצִּיל מִמָּוֶת נַפְשֶׁךָ, כִּי הָרַחְמָנוּת עַל הָרוֹצְחִים שְׁפִיכוּת דָּמִים מִידֵי הָרוֹצְחִים וּמִידֵי אֲחֵרִים הַמִּתְפָּרְצִים: THAT IT MAY GO WELL WITH THEE. The meaning thereof is that avenging innocent blood is a commandment and is a great blessing to you to deliver your soul from death,²⁷⁴Psalms 33:19. because pity upon murderers causes more bloodshed by these murderers and by others who break away [from society].