A consummated sacramental marriage is indissoluble by any human power. Jesus said, “What therefore God has joined together, let not man put asunder” (Mark 10:9). The Catholic Church takes this seriously and therefore will not take part in a new marriage when it believes another valid marriage may already exist. This is true even if that marriage is between Protestants married outside the Catholic Church—such marriages are recognized as valid by the Church. (Note that St. Paul taught of a variance to this—in the case of a marriage between two non-baptized persons when one party later becomes a Christian: “if the unbelieving partner desires to separate, let it be so; in such a case the brother or sister is not bound. For God has called us to peace” [1 Cor. 7:15]. In this case the marriage was not sacramental because the two parties were not baptized.)
Civil divorce is often man’s attempt to put asunder what God has joined together, and the Church knows that man does not have the power or authority to do this. The annulment process is simply the Church’s investigation into what looks like a marriage to determine whether a valid marriage really exists. If it does, the Church will not, indeed cannot, recognize another marriage. If, on the other hand, the Church finds that a valid marriage does not exist, then a new marriage, truly a first marriage (unless a valid previous marriage ended through death), may be celebrated.