The Mass is not Christ re-sacrificed, but re-presented, made present to us. Christ's death happened at one point in history, and the Mass makes the once-for-all death of Christ present for us now at our point in history. The Catechism of the Catholic Church (Catechism of the Catholic Church) expresses this beautifully:

"614 The sacrifice of Christ is unique; it completes and surpasses all other sacrifices"

Catechism of the Catholic Church #614

"1330 The Holy Sacrifice...makes present the one sacrifice of Christ the Savior"

Catechism of the Catholic Church #1330

 Though the death of Christ occurred nearly 2000 years ago, the salvation that resulted from His death is made active in each individual's life when he or she accepts Christ. Christ is not re-sacrificed every time someone becomes born-again in this way. In a similar way, neither do Catholics believe Christ is re-sacrificed at every mass. The sacrifice of Calvary is made present, not repeated.

"1364 When the Church celebrates the Eucharist, she commemorates Christ's Passover, and it is made present: the sacrifice Christ offered once for all on the cross remains ever present"

Catechism of the Catholic Church #1364