Objection 1. It seems that heretics, schismatics, and excommunicated persons are not able to consecrate the Eucharist. For Augustine says (Liber sentent. Prosperi xv) that "there is no such thing as a true sacrifice outside the Catholic Church": and Pope Leo I says (Ep. lxxx; cf. Decretal i, q. 1): Elsewhere "(i.e. than in the Church which is Christ's body) there is neither valid priesthood nor true sacrifice." But heretics, schismatics, and excommunicated persons are severed from the Church. Therefore they are unable to offer a true sacrifice.
Objection 2. Further (Decretal, caus. i, q. 1), Innocent I is quoted as saying: "Because we receive the laity of the Arians and other pestilential persons, if they seem to repent, it does not follow that their clergy have the dignity of the priesthood or of any other ministerial office, for we allow them to confer nothing save Baptism." But none can consecrate the Eucharist, unless he have the dignity of the priesthood. Therefore heretics and the like cannot consecrate the Eucharist.
Objection 3. Further, it does not seem feasible for one outside the Church to act on behalf of the Church. But when the priest consecrates the Eucharist, he does so in the person of the entire Church, as is evident from the fact of his putting up all prayers in the person of the Church. Therefore, it seems that those who are outside the Church, such as those who are heretics, schismatics, and excommunicate, are not able to consecrate the Eucharist.
On the contrary, Augustine says (Contra Parmen. ii): "Just as Baptism remains in them," i.e. in heretics, schismatics, and those who are excommunicate, "so do their orders remain intact." Now, by the power of his ordination, a priest can consecrate the Eucharist. Therefore, it seems that heretics, schismatics, and those who are excommunicate, can consecrate the Eucharist, since their orders remain entire.
I answer that, Some have contended that heretics, schismatics, and the excommunicate, who are outside the pale of the Church, cannot perform this sacrament. But herein they are deceived, because, as Augustine says (Contra Parmen. ii), "it is one thing to lack something utterly, and another to have it improperly"; and in like fashion, "it is one thing not to bestow, and quite another to bestow, but not rightly." Accordingly, such as, being within the Church, received the power of consecrating the Eucharist through being ordained to the priesthood, have such power rightly indeed; but they use it improperly if afterwards they be separated from the Church by heresy, schism, or excommunication. But such as are ordained while separated from the Church, have neither the power rightly, nor do they use it rightly. But that in both cases they have the power, is clear from what Augustine says (Contra Parmen. ii), that when they return to the unity of the Church, they are not re-ordained, but are received in their orders. And since the consecration of the Eucharist is an act which follows the power of order, such persons as are separated from the Church by heresy, schism, or excommunication, can indeed consecrate the Eucharist, which on being consecrated by them contains Christ's true body and blood; but they act wrongly, and sin by doing so; and in consequence they do not receive the fruit of the sacrifice, which is a spiritual sacrifice.
Reply to Objection 1. Such and similar authorities are to be understood in this sense, that the sacrifice is offered wrongly outside the Church. Hence outside the Church there can be no spiritual sacrifice that is a true sacrifice with the truth of its fruit, although it be a true sacrifice with the truth of the sacrament; thus it was stated above (Question 80, Article 3), that the sinner receives Christ's body sacramentally, but not spiritually.
Reply to Objection 2. Baptism alone is allowed to be conferred by heretics, and schismatics, because they can lawfully baptize in case of necessity; but in no case can they lawfully consecrate the Eucharist, or confer the other sacraments.
Reply to Objection 3. The priest, in reciting the prayers of the mass, speaks instead of the Church, in whose unity he remains; but in consecrating the sacrament he speaks as in the person of Christ, Whose place he holds by the power of his orders. Consequently, if a priest severed from the unity of the Church celebrates mass, not having lost the power of order, he consecrates Christ's true body and blood; but because he is severed from the unity of the Church, his prayers have no efficacy.
Source: Summa Theologica (New Advent)