The Mass is not a fresh Sacrifice, nor does the Church teach that it is one.
From the Catechism of the Catholic Church:
From the Council Of Trent, and Vatican 2 documents
“The One that offers Sacrifice is the same One who, after having sacrificed himself on the Cross…to obtain for us eternal redemption…offers Himself now by the ministry of the priest; there is no difference except in the manner of offering.” [Council of Trent, S. 22, c.2]
“For in it Christ perpetuates in an unbloody manner the sacrifice offered on the Cross, offering Himself to the Father for the world’s salvation through the ministry of priests.” [Vatican 2 Documents.9:3]
“perpetrates”, not creates a new thing.
“The Eucharistic Sacrifice is the source and summit of the whole of the Church’s worship and of Christian life. The faithful participate more fully in the sacrament of thanksgiving, propitiation, petition and praise not only when they wholeheartedly offer the sacred Victim, and in it themselves to the Father with the priest, but also when they receive this same Victim sacramentally.” [Vatican 2 Documents :9]
“The other sacraments, as indeed every ministry of the church and every work of the apostolate, are linked with the Eucharist and are directed towards it. For the Eucharist contains the entire spiritual good of the Church, namely, Christ Himself, our Passover and living bread, offering through His flesh, living and life-giving in the Spirit, life to all who are thus invited and led on to offer themselves, their labours, and all created things together with Him.” [Vatican 2 Documents.9:6]
“The faithful are gathered by the preaching of Christ’s Gospel and the mystery of the Lord’s Supper is celebrated, ‘so that through the Body and Blood of the Lord the whole brotherhood is united…Christ is present, by whose power the one, holy, catholic and apostolic Church is united. For the partaking has no less an effect than to change us into what we have received.’” [Vatican 11.9:7. Constitution of the Church, n.26]
“But union with Christ…is not to be limited to the duration of the celebration of the Eucharist; it is to be prolonged into the entire Christian life…(as) a continual thanksgiving under the Holy Spirit and may produce fruits of greater charity.” [Vatican 11.9. iii. 38]