The answer is no.
1)
Not only is it not a mitzva, rather it could be considered a felony. As stated in Devarim 17:7 :
יד העדים תהיה-בו בראשונה, להמיתו, ויד כל-העם, באחרונה; וביערת הרע,
מקרבך
translated by Machon Mamre:
The hand of the witnesses shall be first upon him to put him to death,
and afterward the hand of all the people. So thou shalt put away the
evil from the midst of thee.
2)
In Sanhedrin 73:a, Chazal learn from ולא תעמוד על דם רעך
that one must help and mustn't stand by when one sees someone else is drowning or attacked by a wild animal or the such:
מניין לרואה את חבירו שהוא טובע בנהר או חיה גוררתו או לסטין באין עליו שהוא חייב להצילו ת"ל לא תעמוד על דם רעך
And we can deduce that only חבירו
, a freind, a regular person, or only when the death is not by the lawful eviction of Beit Din - that person should be saved.
3) ADDED IN EDIT
Even if velo ta'amod etc.
is relevant (which I claim to the contrary), it's only one negative commandment that conflicts with 2 other commandments, one is positive - to punish - and the other is to do what the Chachamim say (Devarim 17:10-11: וְשָׁמַרְתָּ לַעֲשׂוֹת כְּכֹל אֲשֶׁר יוֹרוּךָ. עַל פִּי הַתּוֹרָה אֲשֶׁר יוֹרוּךָ וְעַל הַמִּשְׁפָּט אֲשֶׁר יֹאמְרוּ לְךָ תַּעֲשֶׂה לֹא תָסוּר מִן הַדָּבָר אֲשֶׁר יַגִּידוּ לְךָ יָמִין וּשְׂמֹאל
) - which could be either a negative commandment, a positive, or both altogether (it doesn't matter for this claim).
Genrally, the gemara in Menahot 40:a says:
דאמר ריש לקיש כל מקום שאתה מוצא עשה ולא תעשה אם אתה יכול לקיים את שניהם מוטב ואם לאו יבוא עשה וידחה את לא תעשה
as said Resh Lakish everywhere you find Aseh and Lo Ta'aseh, if you can do both, great, otherwise, comes the Aseh and rejects the Lo Ta'aseh
so velo ta'amod etc.
should be overruled.
Specifically, the pshat of ולא תעמוד על דם רעך
(Vayikra 19:16) relates your freind. A death-senteced man isn't considered a typical freind. I coudn't find explicit sources for this commentary on this exact verse, but I did find that רעך
isn't just anyone.
In Vayikra 19:13, לא-תעשוק את-רעך
(Thou shalt not oppress thy neighbour
), Chazal explain in Bava-Metzia 111:b that רעך
is either used to exclude Ger Toshav or to exclude a man from the people of Amaleq.
In Shmot 2:13, Moses says to the Israeli that's about to hit another Israeli: וַיֹּאמֶר, לָרָשָׁע, לָמָּה תַכֶּה, רֵעֶךָ
(Machon Mamre trans.: and he said to him that did the wrong: 'Wherefore smitest thou thy fellow?'
), and Rashi explains:
רעך - רשע כמותך.
which is, in other words, "his your freind in his behavior", you guys behave the same. So when the term רעך
is used in non-negative context, it's assumed to withold well-begaving person.
my free translation:
thy fellow - bad like yourself.