http://www.newadvent.org/cathen/05054c.htm
3. The Dogmatic Basis and Practical Application of The Complete Dissolubility of Consummated Marriage within the Catholic Church
(a) Its Foundation in Scripture — The complete exclusion of absolute divorce (divortium perfectum) in Christian marriage is expressed in the words quoted above (Mark 10; Luke 16; 1 Corinthians 7). The words in St. Matthew's Gospel (xix, 9), "except it be for fornication", have, however, given rise to the question whether the putting-away of the wife and the dissolution of the marriage bond were not allowed on account of adultery. The Catholic Church and Catholic theology have always maintained that by such an explanation St. Matthew would be made to contradict Sts. Mark, Luke, and Paul, and the converts instructed by these latter would have been brought into error in regard to the real doctrine in Christ. As this is inconsistent both with the infallibility of the Apostolic teaching and the inerrancy of Sacred Scripture, the clause in Matthew must be explained as the mere dismissal of the unfaithful wife without the dissolution of the marriage bond. Such a dismissal is not excluded by the parallel texts in mark and Luke, while Paul (1 Corinthians 7:11) clearly indicates the possibility of such a dismissal: "And if she depart, that she remain unmarried, or be reconciled to her husband".Grammatically, the clause in St. Matthew may modify one member of the sentence (that which refers to the putting-away of the wife) without applying to the following member (the remarriage of the other), though we must admit that the construction is a little harsh. If it means, "Whoever shall put away his wife, except it be for fornication, and shallmarry another, commiteth adultery", then, in case of marital infidelity, the wife may be put away; but that, in this case, adultery is not committed by a new marriage cannot be concluded from these words. The following words, "And he that shall marry her that is put away" — therefore also the woman who is dismissed for adultery — "committeth adultery", say the contrary, since they suppose the permanence of the first marriage. Moreover, the brevity of expression in Matthew 19:9, which seems to us harsh, is explicable, because the Evangelist had previously given a distinct explanation of the same subject, and exactly laid down what was justified by the reason of fornication: "Whosoever shall put away his wife, excepting for the causes of fornication, maketh her to commit adultery: and he that shall marry her that is put away, committeth adultery" (Matthew 5:32). Here all excuse for remarriage or for the dissolution of the first marriage is excluded. Even the mere dismissal of the wife, if this is done unjustly, exposes her to the danger of adultery and is thus attributed to the husband who has dismissed her — "he maketh her commit adultery". It is only in the case of marital infidelity that complete dismissal is justified — "excepting for the cause of fornication". In this case not he, but the wife who has been lawfully dismissed, is the occasion, and she will therefore be responsible should she commit further sin. It must also be remarked that even for Matthew 19:9, there is a variant reading supported by important codices, which has "maketh her to commit adultery" instead of the expression "comitteth adultery". This reading answers the difficulty more clearly. (Cf. Knabenbauer, "Comment, in Matt.", II, 144).
The question on the certificate of divorce comes from Deut. 24:1-4 and what is described there is the ending, the dissolution of the marriage, not the “mere dismissal” of the wife. The so divorced woman was freed to become another man's wife. Given that the penalty for adultery was death the law allowing a certificate of divorce would hardly facilitate it.
Jesus’ words at Matt. 19 clearly state the one exception that allowed divorce, not on every account, but on the one he cited, fornication. What the article calls “complete dismissal” isn't clear.
Paul's words at I Cor. 7 dealt not with dismissal or divorce but with whether, in his recommendation of singleness, it was proper for a married person to leave their partner.
According to Jesus’ words "porneia, fornication" constituted grounds for ending the marriage by the offended party.