Ecumenical Councils of the Church
The Ecumenical Council of Ephesus (431) teaches, “He (Christ) offered Himself for us as a sweet odor (that is, a pleasing sacrifice) to the God and Father.”
The Ecumenical Council of Trent (1545), in its authoritative teaching on the Sacrifice of the Mass, presupposes that Christ’s death on the cross was a sacrifice, calling it an “oblation” on the “altar of the cross.” None of the other 19 Ecumenical Councils of the Church have contradicted these teachings, including the Second Vatican Council.
The Catechism of the Catholic Church
The Catechism of the Catholic Church sums up the Church’s teaching nicely:
Christ’s death is both the Paschal sacrifice that accomplishes the definitive redemption of men, through “the Lamb of God, who takes away the sin of the world”, and the sacrifice of the New Covenant, which restores man to communion with God by reconciling him to God through the “blood of the covenant, which was poured out for many for the forgiveness of sins”.
This sacrifice of Christ is unique; it completes and surpasses all other sacrifices. First, it is a gift from God the Father himself, for the Father handed his Son over to sinners in order to reconcile us with himself. At the same time it is the offering of the Son of God made man, who in freedom and love offered his life to his Father through the Holy Spirit in reparation for our disobedience.
For as by one man’s disobedience many were made sinners, so by one man’s obedience many will be made righteous.” By his obedience unto death, Jesus accomplished the substitution of the suffering Servant, who “makes himself an offering for sin”, when “he bore the sin of many”, and who “shall make many to be accounted righteous”, for “he shall bear their iniquities”. Jesus atoned for our faults and made satisfaction for our sins to the Father. {CCC 613-615]
Sacred Scriptures
Sacred Scriptures are replete with evidence that Christ’s death was sacrificial:
“even as the Son of man came not to be served but to serve, and to give his life as a ransom for many.” Matthew 20:28
“For there is one God, and there is one mediator between God and men, the man Christ Jesus, who gave himself as a ransom for all, the testimony to which was borne at the proper time. 1 Timothy 2:5-6
“and they sang a new song, saying, “Worthy art thou to take the scroll and to open its seals, for thou wast slain and by thy blood didst ransom men for God from every tribe and tongue and people and nation” Revelation 5:9
“Then he took a cup, and when he had given thanks he handed it to them saying, ‘Drink from this, all of you, for this is my blood, the blood of the covenant, poured out for many for the forgiveness of sins.” Matthew 26:27-28 NJB Jesus used sacrificial words such as “body”, “blood”, “poured”, “offered” and “given” at the Last Supper. Moreover, when he lifted the cup and spoke of the “blood of the covenant” he was echoing Moses’ words when he sealed the Old Covenant with a sacrifice on Mt. Sinai. (Exodus 24:8)
“The next day, he saw Jesus coming towards him and said, ‘Look, there is the lamb of God that takes away the sin of the world.” John 1:29 NJB
“…and follow Christ by loving as he loved you, giving himself up for us as an offering and a sweet-smelling sacrifice to God.” Ephesians 5:2 NJB
“Throw out the old yeast so that you can be the fresh dough, unleavened as you are. For our Passover has been sacrificed, that is, Christ;” 1 Corinthians 5:7 NJB
“God appointed him as a sacrifice for reconciliation, through faith, by the shedding of his blood, and so showed his justness; first for the past, when sins went unpunished because he held his hand;” Romans 3:25 NJB