The Congregation for the Doctrine of the Faith published a very very brief document on the subject in 2001. The entire text of the English translation is:
Question: Whether the baptism conferred by the community «The Church of Jesus Christ of Latter-day Saints», called «Mormons» in the vernacular, is valid.
The Supreme Pontiff John Paul II, in the Audience granted to the undersigned Cardinal Prefect, approved the present Response, decided in the Sessione Ordinaria of this Congregation, and ordered it published.
From the Offices of the Congregation for the Doctrine of the Faith, 5 June 2001.
The Congregation did also issue a brief commentary on the decision, written by Father Luis Ladaria. In it, Father Ladaria explained that the issue was largely not because of the wording of the baptismal formula, but because of the theology behind it. In his words,
The formula used by the Mormons might seem at first sight to be a Trinitarian formula. The text states: "Being commissioned by Jesus Christ, I baptize you in the name of the Father, and of the Son, and of the Holy Spirit" (cf. D&C 20:73). The similarities with the formula used by the Catholic Church are at first sight obvious, but in reality they are only apparent. There is not in fact a fundamental doctrinal agreement. There is not a true invocation of the Trinity because the Father, the Son and the Holy Spirit, according to the Church of Jesus Christ of Latter-day Saints, are not the three persons in which subsists the one Godhead, but three gods who form one divinity. ... God the Father has a wife, the Heavenly Mother, with whom he shares the responsibility of creation. They procreate sons in the spiritual world. Their firstborn is Jesus Christ, equal to all men, who has acquired his divinity in a pre-mortal existence. Even the Holy Spirit is the son of heavenly parents. The Son and the Holy Spirit were procreated after the beginning of the creation of the world known to us (cf. EM, Vol. 2, p. 961). Four gods are directly responsible for the universe, three of whom have established a covenant and thus form the divinity.
As is easily seen, to the similarity of titles there does not correspond in any way a doctrinal content which can lead to the Christian doctrine of the Trinity. The words Father, Son and Holy Spirit, have for the Mormons a meaning totally different from the Christian meaning.
Father Ladaria admits that "doctrinal errors usually do not invalidate baptism ... because whoever is baptized in the name of Christ, wherever that has taken place, has received the grace of Christ"; but a valid baptism, in the Church's eyes, requires "the intention to do what the Church wants, what Christ wants". Since by "Christ" the Church of Jesus Christ of Latter-Day Saints means something quite different than what the Catholic Church means:
The Mormon minister, who must necessarily be the "priest" (cf. D&C 20:38-58.107:13.14.20), therefore radically formed in their own doctrine, cannot have any other intention than that of doing what the Church of Jesus Christ of Latter-day Saints does, which is quite different in respect to what the Catholic Church intends to do when it baptizes, that is, the conferral of the sacrament of Baptism instituted by Christ, which means participation in his death and resurrection (cf. Rom 6,3-11; Col 2,12-13)
it follows that the baptism conferred by this community is not a valid baptism.