Sukkos as days of refinement and salvation

סוכות המה ימי ישועה לכן קבעו בהם הושענות.

Sukkos are days of yeshuah (salvation); therefore the Hoshanos were established for them.

The Sefas Emes sets out his theme: Sukkos is essentially a time of deliverance, which is why we cry out "Hoshana" — "save us" — throughout the festival.

דאיתא מלך ממית ומחיה ומצמיח ישועה.

For it is taught that the King "puts to death and gives life and causes salvation to sprout."

Drawing on the language of the Shemoneh Esrei, he notes that Hashem's kingship works in stages — first removing, then reviving, then bringing forth deliverance.

וכל זה מתקיים בימים אלו ר"ה ויוהכ"פ וסוכות.

And all of this is fulfilled in these days — Rosh Hashanah, Yom Kippur, and Sukkos.

This threefold process of death, revival, and salvation plays out across the Yamim Noraim and culminates in Sukkos.

וע"י שנתבררו בני ישראל בימי הדין והוסר מהם הפסולת.

And through Bnei Yisrael being refined during the Days of Judgment, the dross is removed from them.

The Yamim Noraim are a process of birur (refinement) in which the impurity clinging to a person is burned away.

שזה הג' ספרים.

This is the meaning of the three books.

He alludes to Chazal's teaching that on Rosh Hashanah three books are opened — for the wholly righteous, the wholly wicked, and those in between (Rosh Hashanah 16b).

רשעים גמורים לאלתר למיתה שהוא הפסולת שאין בו טוב.

The completely wicked are inscribed immediately for death — for they are the dross in which there is no good.

What is utterly devoid of good, having no spark to be redeemed, is what must be cut away — this is the "death" of the refining process.

ולזה הסט"א ה' ממית כדאיתא בזוה"ק על פסוק ה' ממית כו'.

And to this — the sitra achra (the "other side") — applies "Hashem puts to death," as is brought in the Zohar on the pasuk "Hashem puts to death."

The "death" Hashem brings is aimed at the sitra achra, the force of impurity, which must be stripped away (Shmuel I 2:6).

שא"י לעלות למקום המוכן לו בג"ע עד שהוסר כח הסט"א.

For a person cannot ascend to the place prepared for him in Gan Eden until the power of the sitra achra has been removed.

The soul cannot rise to its destined portion while the husk of impurity still clings to it; the negative force must first be cleared away.

כן צריכין להתטהר מקודם בימי הדין שנוכל לכנוס אח"כ בצלו ית':

So too we must first purify ourselves during the Days of Judgment, so that we may afterward enter into His shade, may He be blessed.

Just as the soul is cleansed before entering Gan Eden, so the avodah of the Yamim Noraim purifies us so that we can then enter the Sukkah — "His shade" — in closeness to Hashem.

Summary: Sukkos is the festival of salvation, the culmination of a refining process that begins on Rosh Hashanah and Yom Kippur. Just as Hashem's kingship "puts to death, gives life, and brings forth salvation," the Yamim Noraim strip away the dross and the power of the sitra achra, purifying Bnei Yisrael so that they can finally enter into the shade of Hashem in the Sukkah.