“May you cast to the sea-depths all our sins!”
These words are well-known to observant Jews because they form the basis of the Tashlikh ceremony of the afternoon of the first day of Rosh HaShanah in which this text is symbolically re-enacted. It is of course an excellent practice to inflect a text not only on a verbal level, but on a physical level. Kinetic learning is a trait of all full-bodied religion (pun intended).
Sephardic Jews recite Micah 7:18-20 together with Hosea 14:2-10 on Shabbat Shuvah (the Sabbath before Yom Kippur). All Jews recite it, together with the entire book of Jonah, as a Haftarah on Yom Kippur Afternoon.
The Masoretic text reads ‘their sins,’ not ‘our sins’ in 7:19. ‘Their sins’ seems to fit the context poorly, and might be accounted for in terms of scribal error (נו corrupted to מ). The Old Greek translates as if its source text read ‘our sins.’ The reading was independently reproposed in gaonic times. I have adopted the proposal here.
כִּי־חָפֵץ חֶסֶד הוּא
וְתַשְׁלִיךְ בִּמְצֻלוֹת יָם
תִּתֵּן אֱמֶת לְיַעֲקֹב
אֲשֶׁר נִשְׁבַּעְתָּ לַאֲבֹתֵינוּ
Who is a god like you,
a forgiver of sin,
who overlooks transgression
of the remnant of his heritage?
He does not hold onto
his anger forever,
for he takes delight in kindness.
He will again have compassion on us,
and tread our iniquity underfoot.
May you cast to the sea-depths
all our offenses.
May you show faithfulness to Yaacov,
kindness to Avraham
as you promised our ancestors
in days long ago.
The keyword here is חסד. It is variously translated: ‘clemency’ (NRSV); ‘mercy’ (REB); ‘faithful love’ (NJB), ‘steadfast love’ (ESV), and ‘unchanging love’ (NASB). But NJPSV catches the nuance best with ‘kindness.’ God, it is confessed, is more than faithful to his promises. He goes beyond them, and in fact ignores them, for he shows kindness where, according to his promises, he was to have shown rigor.
 Michael Fishbane, Haftarot (JPSBC; Philadelphia: Jewish Publication Society, 2002) 391, 491.