Not that I would presume to explain Rabbi Vital's words or the teachings of the Ari z"l, but in context it seems to be alluding to the expression found in the name of Rav Kahana in tractate Chullin 27a which says:
אמר רב כהנא מנין לשחיטה שהיא מן הצואר שנאמר (ויקרא א, ה) ושחט את בן הבקר ממקום ששח חטהו ממאי דהאי חטהו לישנא דדכויי הוא דכתיב (ויקרא יד, מט) וחטא את הבית ואיבעית אימא מהכא (תהלים נא, ט) תחטאני באזוב ואטהר
That the text from Eitz Chayim you quote is relating this to the Tzimtzum HaRishon at the very beginning of Creation. That this Tzimtzum is also called the Lamp of Darkness like the Cleansing place of Darkness.
That in kabbalistic teaching this Tzimtzum is the concealment of the Infinite, simple and undifferentiated Light(אור אין סוף) at the beginning of Creation. This results in what appears to be the absence of light, or Darkness. Like the text states explicitly, this is the root of Judgement (also called Gevurah) and is the source of all the discrete worlds or universes which follow, meaning separate exist apart from G-d's absolute oneness (יש מאין).
That in keeping with what Rav Kahana is saying, this (the Tzimtzum HaRishon) parallels the place of ritual slaughter at the throat which is also the source point for the simple, undifferentiated sound or voice of the animal.
And continuing that analogy, in the human being, who is comprised of both an Animal (or animating) Soul and a G-dly Soul, that simple sound is then differentiated into the letters and words of speech (which make up prayer and Torah study) via the five parts of the mouth. Those five parts of the mouth correspond with the five Gevurot and their corresponding five Chassadim. That is why this expression carries the dual meaning of dressing in a garment which conceals and also cleansing through words of Torah and prayer.
For details of this word meaning, see Jastrow, definition I for חטה, חטא, חטי, in Binyan Pi'el which pertain to dressing and cleansing and definition II which pertains to the idea of seduction and sin.
This second definition relates to the allegory used by the Ari z"l comparing the Yetzer HaRah to a Harlot who is also a loyal subject of the King. The King sends the Harlot to tempt his son in order to reveal the superior qualities of the son. The Harlot, being a loyal servant of the King, obeys, but all the while hopes the son will resist the temptation. In this context, חטה is also related linguistically to נטה, נטי in Binyan Hifal (חיטה) like is brought in Jastrow.
And see also Sefer Kehillat Yaacov by Rabbi Yaacov Tzvi Yolles in relation to:
קדר That as pointed out in Jastrow, קרדונין is also understood as קדרינון, meaning קדר ינון, the Darkness of Yinon. That Yinon is one of the names of Moshiach alluded to in Bereshit 1:2. See Tehillim 72:17, Bereshit Rabbah 1:4 and Sanhedrin 98b:14.
חטה:א And just to emphasize that based upon the explanation from Rabbi Yolles, חטי would be emphasizing both the 22 simple letters of the Aleph-Beit and the 5 final letters of מנצפ״ך.
חטה:ד (The emphasis here is that this root relates to G-d's name from the side of Chesed (מפי החסד), namely טדה״ט.