Mitzvos draw the neshamah's life into the body

וכתי' אשר יעשה אותם האדם וחי בהם.

And it is written: "which a person shall do and live by them."

The Sefas Emes begins with the pasuk about the mitzvos, "and live by them," which he will explain as drawing life into the body.

שהמצות ממשיכין החיות להאברים כדאיתא רמ"ח מ"ע נגד רמ"ח אברים.

For the mitzvos draw vitality (chiyus) into the limbs, as it is taught: the 248 positive mitzvos correspond to the 248 limbs.

Each of the 248 positive mitzvos channels life into a corresponding limb of the body, animating the person through Torah.

ובגמ' מכל החי שחיין ראשי אברים שבה.

And in the Gemara: "of every living thing" — that the tips of its limbs are alive.

The Gemara derives that a fit korban must have living, intact limb-tips, teaching that true "life" reaches all the way to the extremities.

וממעט מחוסר אבר להקרבה.

And it excludes an animal missing a limb from being offered as a korban.

An animal lacking a limb is disqualified for the Mizbe'ach, because the offering must be whole and fully alive.

כמו כן וחי בהם להיות חיים ראשי האברים דכתי' ויפח באפיו נשמת חיים ויהי האדם לנפש חי'.

So too "and live by them" — that even the tips of the limbs should be alive, as it is written "and He breathed into his nostrils the breath of life, and man became a living soul."

Just as a korban must be wholly alive, the mitzvos make the entire person — to his very extremities — fully alive with the neshamah Hashem breathed into him.

פי' שהוא כלי להמשיך חיות הנשמה לתוך כל האברים.

The meaning is that man is a vessel (keli) to draw the vitality of the neshamah into all the limbs.

The body's purpose is to serve as a vessel, conducting the life of the neshamah outward into every limb.

והנה קודם חטא אדה"ר הי' כולו חי וע"י החטא בא המיתה מצד הגוף.

Now before the sin of Adam HaRishon he was entirely alive, and through the sin death came by way of the body.

Originally man was wholly suffused with life; the cheit introduced death, which entered specifically through the physical body.

וכתי' ויגרש את האדם וכל הענין להט החרב המתהפכת.

And it is written "and He drove out the man," and the whole matter of "the flame of the ever-turning sword."

After the sin, man was banished from Gan Eden, with the turning sword of flame barring the way back to the Eitz HaChaim.

הכל הוא באדם עצמו שנעשה מסך מבדיל בין הנפש ונשמה שרומז לג"ע ולעץ החיים ובין הגוף.

All of this is within man himself, that a separating partition (masach mavdil) was formed between the nefesh and neshamah — which allude to Gan Eden and the Eitz HaChaim — and the body.

The "banishment" is internal: the sin erected a barrier inside man, cutting off his body from the inner life of his nefesh and neshamah, which represent Gan Eden and the Tree of Life.

אבל הקב"ה שבחר בנו ונתן לנו תורה ומצות פתח לנו פתח להתדבק בעה"ח ולהמשיך חיות הנשמה להאברים ע"י המצות.

But Hashem, who chose us and gave us Torah and mitzvos, opened for us an opening to cling to the Eitz HaChaim and to draw the vitality of the neshamah into the limbs through the mitzvos.

Torah and mitzvos reopen the path that the sin had sealed, allowing a Jew to reconnect to the Tree of Life and bring the neshamah's life back into his body.

נר מצוה ותורה אור האברים והנפש:

"A mitzvah is a candle and the Torah is light" — for the limbs and for the nefesh.

Mitzvah and Torah illuminate both the physical limbs and the inner nefesh, reuniting body and soul in living light.

Summary: The mitzvos are the channels that draw the life of the neshamah into the body's 248 limbs, just as a korban must be wholly alive. The sin of Adam erected an inner barrier separating body from soul and brought death; Torah and mitzvos reopen the path to the Eitz HaChaim, restoring life to limbs and nefesh alike — "a mitzvah is a candle and the Torah is light."