In this prayer, you’re asking God to show mercy to the world and give people graces for conversion, because of His Son’s sacrifice. You are offering Christ to the Father, so that “for the sake of His sorrowful Passion” He will show mercy to the world.
In an earlier response, it was stated with reference to the mass, that “we can’t offer the Sacrifice of the Mass like a priest does,”. This is true; we have no power to change a mere piece of bread into the body of Christ, nor wine into His blood. However, we participate with the priest, in offering to the Father, the sacrifice of the body and blood of Christ through the power of the priest to consecrate the bread and wine.
So it is with the words of the prayer you quoted. It is Jesus Christ, Himself, who offered his Body and Blood, Soul and Divinity, to the Father, but it is we who participate in this offering every time we say these words with reverence, to the Father.
We give back to the Father, that which he gave us, the unfathomable sacrifice of his son, as we utter the words of this prayer. It is a humble acknowledgement of the incomprehensible gift given to us, and of the indescribable glory that is the Most High.