St. Thomas Aquinas
“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 (Q[79], A[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 Heb. 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.”
Source: St. Thomas Aquinas, Summa Theologica