In reverse order,
Q2:
Where does he get this from
Rav Hinana (Baba Mesia 59a) describes the scope of the prohibition as only applying to shomre miswoth (those observant of miswoth), as only they are properly called עמיתו:
אמר רב חננא בריה דרב אידי: מאי דכתיב "ולא תונו איש את עמיתו" – עם שאתך
בתורה ובמצוות אל תונהו"
Rav Hinana, son of Rav Idi, says: What is the meaning of that which is
written: “And you shall not mistreat each man his colleague
('amitho)”? [The word 'amitho is interpreted as a contraction of 'im
ito, meaning: One who is with him.] With [one who is] with you in
[observance of] Torah and miswoth, you shall not mistreat him.
The Hagahoth Maimonioth (H. Mekhirah 14, 4) wrote:
תניא ולא תונו איש את עמיתו עם שאתך בתורה ובמצות לא תונהו. למדנו שלא
הזהיר הכתוב באונאת דברים אלא ירא השם. ואמר במדרש, שאם הונה עצמו, אתה
רשאי להונהו, שאין קרוי עמיתך
It was taught that you should not mistreat your colleague if he is with
you in Torah and miswoth. We have learned that the Torah does not warn
against Onath Debharim except against those who awe God. And the
Midrash says, that if he mistreats himself you are permitted to
mistreat him, for he is not called your colleague.
Q1:
how can a passuk in Nach supercede an issur in the Torah?
When R. Yonah quotes Mishle, this serves merely as a sort of asmakhta. It is not the source of the law (the scope of which is defined above), rather it is scriptural allusion that resonates with the same/similar concept. Accordingly, this ought not be interpreted as an occasion where a passage in Nakh is being used to supercede a Torah prohibition.
In the comments you write regarding R. Yonah's position that:
It seems as though... he's referring to a case of a one time sin...
that would be pretty extreme to categorize him as יצא מכלל עמיתך - for
the one sin
R. Yonah states (Gate 3, sec. 219):
ואם החוטא איש אשר איננו ירא מלפני האלהים. כמו הפורק מעליו עול מלכות
שמים. ואינו נזהר מעבירה אחת אשר כל שער עמו יודע כי היא עבירה. מותר
להכלימו ולספר בגנותו. כך אמרו רבותינו (ויקרא כ״ה:י״ז) אל תונו איש את
עמיתו. עם שאתך בתורה ובמצות אל תונהו בדברים. ואשר לא שת לבו אל דבר ה'
מותר להכלימו במעלליו ולהודיע תועבותיו ולשפוך בוז עליו. ועוד אמרו
מפרסמין את החנפים מפני חלול השם. אבל אם נכשל בחטא על דרך מקרה. ורוב
הימים דרכו להשתמר מעונו. אין לגלות על חטאו
And if the sinner is one who does not fear God, such as one who casts
off from himself the yoke of the Kingdom of Heaven, and is not heedful
of a certain transgression which is known to be a transgression by all
the others of his fellow men, it is permitted to humiliate him and to
speak degradingly of him. As our Sages have said in relation to the
verse, "and ye shall not wrong one another" - "If one is with you in
Torah and miswoth, you shall not wrong him with words." If one however
does not apply his heart to the word of God, it is permitted to
humiliate him through his deeds, to make known his abominations, and
to pour shame upon him. And they have said further. "Hypocrites should
be exposed to prevent desecration of the Name". But if one falls into
sin by chance, and most of his days is wont to guard himself against
transgression, his sin should not be revealed.
Making it clear, that in his estimation it is inapplicable to a single fleeting sin, but rather to a specific type of character with an entire disposition of the personality. In order to be open to such criticism, this individual must flagrantly violate a law which is undeniably known by all of his coreligionists, do so as a pattern of behavior, and in a way that demonstrates that he is פורק מעליו עול מלכות שמים (casts off from upon himself the yoke of heaven).
This type of individual (הפורק עול) is described in greater detail by R. Yonah earlier (Gate 3, sec. 143):
וענין הפורק עול כגון הכופר לאכול נבילות או לאכול חלב ודם או לחלל
יו"ט. ואף על פי שאינו עובר על שאר המצות. אחרי אשר הסיר מעליו עול אזהרה
אחת, כבר מרד בשם יתעלה. אמנם כי גם פעמים הצדיקים נכשלים בחטא אחד אבל
אין זה בלתי על דרך מקרה. בהתגבר עליו היצר. ונפשו מרה לו על הדבר. ונזהר
ממנו אחרי כן. אבל האומר בלבבו לפרוק מעליו עול אזהרה אחת כל עת אשר
יתאוה לעבור הוא הנקרא כופר לדבר א'.
"Removal of the yoke" refers to a denial by which one permits to
himself such things as eating a carcass, suet, or blood, and
desecrating the festivals. Although he does not transgress the other
miswoth, still, by having removed from himself the yoke of one of
exhortation, he has rebelled against the blessed Name. It cannot be
denied that the righteous, also, sometimes go astray in respect to a
particular sin, but when they do, it is the result of circumstances,
of their having been overpowered by the evil inclination, and they are
bitter over what they have done, and keep from doing so again. But one
who entertains in his heart the thought of removing from himself the
yoke of one exhortation whenever he desires to transgress, is called
"an unbeliever in respect to one thing."
