Good question! In the New American Bible (Revised Edition), which is the translation authorized by the U.S. Council of Catholic Bishops for use in the United States, Matt. 19:9 reads:
I say to you, whoever divorces his wife (unless the marriage is unlawful) and marries another commits adultery.
(Note: you don't specify which translation you're using; that would be helpful information.)
It would be interesting to know what the original Greek says; I may search for or post a question on Biblical Hermeneutics about that.
The NABRE has a note on the verse, referring to a note on Matt. 5:31–32. That note reads:
(Unless the marriage is unlawful): this “exceptive clause,” as it is often called, occurs also in Mt 19:9, where the Greek is slightly different. There are other sayings of Jesus about divorce that prohibit it absolutely (see Mk 10:11–12; Lk 16:18; cf. 1 Cor 7:10, 11b), and most scholars agree that they represent the stand of Jesus. Matthew’s "exceptive clauses" are understood by some as a modification of the absolute prohibition. It seems, however, that the unlawfulness that Matthew gives as a reason why a marriage must be broken refers to a situation peculiar to his community: the violation of Mosaic law forbidding marriage between persons of certain blood and/or legal relationship (Lv 18:6–18). Marriages of that sort were regarded as incest (porneia), but some rabbis allowed Gentile converts to Judaism who had contracted such marriages to remain in them. Matthew’s “exceptive clause” is against such permissiveness for Gentile converts to Christianity; cf. the similar prohibition of porneia in Acts 15:20, 29. In this interpretation, the clause constitutes no exception to the absolute prohibition of divorce when the marriage is lawful.
Thus, it appears that Catholic interpretation of this particular passage considers the statement in Matthew to refer to a specific situation present uniquely in Matthew's community at the time, and thus not applicable generally, and gives precedence to the alternate statements on divorce present in the other synoptic gospels.
The Catechism of the Catholic Church agrees with this interpretation:
Divorce is a grave offense against the natural law. It claims to break the contract, to which the spouses freely consented, to live with each other till death. Divorce does injury to the covenant of salvation, of which sacramental marriage is the sign. Contracting a new union, even if it is recognized by civil law, adds to the gravity of the rupture: the remarried spouse is then in a situation of public and permanent adultery:
If a husband, separated from his wife, approaches another woman, he is an adulterer because he makes that woman commit adultery; and the woman who lives with him is an adulteress, because she has drawn another’s husband to herself.
(CCC, paragraph 2384. The quoted section is cited as "St. Basil, Moralia 73, 1".)
This is why the Church is so forcefully against divorce.