Objection 1. It seems that Christ is not sacrificed in the celebration of this sacrament. For it is written (Hebrews 10:14) that "Christ by one oblation hath perfected for ever them that are sanctified." But that oblation was His oblation. Therefore Christ is not sacrificed in the celebration of this sacrament.
Objection 2. Further, Christ's sacrifice was made upon the cross, whereon "He delivered Himself for us, an oblation and a sacrifice to God for an odor of sweetness," as is said in Ephesians 5:2. But Christ is not crucified in the celebration of this mystery. Therefore, neither is He sacrificed.
Objection 3. Further, as Augustine says (De Trin. iv), in Christ's sacrifice the priest and the victim are one and the same. But in the celebration of this sacrament the priest and the victim are not the same. Therefore, the celebration of this sacrament is not a sacrifice of Christ.
On the contrary, Augustine says in the Liber Sentent. Prosp. (cf. Ep. xcviii): "Christ was sacrificed once in Himself, and yet He is sacrificed daily in the Sacrament."
I answer that, The celebration of this sacrament is called a sacrifice for two reasons. First, because, as Augustine says (Ad Simplician. ii), "the images of things are called by the names of the things whereof they are the images; as when we look upon a picture or a fresco, we say, 'This is Cicero and that is Sallust.'" But, as was said above (Question 79, Article 1), the celebration of this sacrament is an image representing Christ's Passion, which is His true sacrifice. Accordingly the celebration of this sacrament is called Christ's sacrifice. Hence it is that Ambrose, in commenting on Hebrews 10:1, says: "In Christ was offered up a sacrifice capable of giving eternal salvation; what then do we do? Do we not offer it up every day in memory of His death?" Secondly it is called a sacrifice, in respect of the effect of His Passion: because, to wit, by this sacrament, we are made partakers of the fruit of our Lord's Passion. Hence in one of the Sunday Secrets (Ninth Sunday after Pentecost) we say: "Whenever the commemoration of this sacrifice is celebrated, the work of our redemption is enacted." Consequently, according to the first reason, it is true to say that Christ was sacrificed, even in the figures of the Old Testament: hence it is stated in the Apocalypse (13:8): "Whose names are not written in the Book of Life of the Lamb, which was slain from the beginning of the world." But according to the second reason, it is proper to this sacrament for Christ to be sacrificed in its celebration.
Reply to Objection 1. As Ambrose says (commenting on Hebrews 10:1), "there is but one victim," namely that which Christ offered, and which we offer, "and not many victims, because Christ was offered but once: and this latter sacrifice is the pattern of the former. For, just as what is offered everywhere is one body, and not many bodies, so also is it but one sacrifice."
Reply to Objection 2. As the celebration of this sacrament is an image representing Christ's Passion, so the altar is representative of the cross itself, upon which Christ was sacrificed in His proper species.
Reply to Objection 3. For the same reason (cf. Reply to Obj. 2) the priest also bears Christ's image, in Whose person and by Whose power he pronounces the words of consecration, as is evident from what was said above (82, 1,3). And so, in a measure, the priest and victim are one and the same.
Source: Summa Theologica (New Advent)