This?:

"Because we murdered You, have mercy on us and on the whole world."

The "for the sake of" part confuses me. Help.

Some [if not most] of the best Catholic prayers were originally written in Latin or Greek, so a vernacular translation sometimes cannot literally convey the precise meaning of certain ablative and prepositional phrases that may be crucial for the meaning of the entire text.

By that prayer, we mean to offer the Eternal Father the infinite merits of the Passion of His only-begotten Son, Who became incarnate in the chaste womb of Mary Most Holy to redeem the human race. The expiatory sufferings of Our Lord placated the divine wrath incurred by original and actual sin of the human race as a whole, and each human person individually. The Passion of Our Lord was more well-pleasing before the Father than the sins of all mankind were displeasing to Him, because of the divine dignity of the God-Man. The Eternal Father in sending His only-begotten Son into the world also manifested the infinite charity wherewith He has loved us.

When we address this prayer to the Christ, it is to prayerfully remind Him to grant us grace and have mercy upon us by reason of the infinite and eternal love that lead Him to utter desolation and annihilation upon Mount Calvary. It is on His infinite merits, not on our own (we can call nothing our own save our sins and demerits) that we must always rely. We deserve nothing but chastisement, and grace is given only by Christ's most holy Passion.