Objection 1. It would seem that schismatics have some power. For Augustine says (Contra Donat. i, 1): "Just as those who come back to the Church after being baptized, are not baptized again, so those who return after being ordained, are not ordained again." Now Order is a kind of power. Therefore schismatics have some power since they retain their Orders.
Objection 2. Further, Augustine says (De Unico Bapt. [De Bap. contra Donat. vi, 5): "One who is separated can confer a sacrament even as he can have it." But the power of conferring a sacrament is a very great power. Therefore schismatics who are separated from the Church, have a spiritual power.
Objection 3. Further, Pope Urban II [Council of Piacenza, cap. x; cf. Can. Ordinationes, ix, qu. 1 says: "We command that persons consecrated by bishops who were themselves consecrated according to the Catholic rite, but have separated themselves by schism from the Roman Church, should be received mercifully and that their Orders should be acknowledged, when they return to the unity of the Church, provided they be of commendable life and knowledge." But this would not be so, unless spiritual power were retained by schismatics. Therefore schismatics have spiritual power.
On the contrary, Cyprian says in a letter (Ep. lii, quoted vii, qu. 1, can. Novatianus): "He who observes neither unity of spirit nor the concord of peace, and severs himself from the bonds of the Church, and from the fellowship of her priests, cannot have episcopal power or honor."
I answer that, Spiritual power is twofold, the one sacramental, the other a power of jurisdiction. The sacramental power is one that is conferred by some kind of consecration. Now all the consecrations of the Church are immovable so long as the consecrated thing remains: as appears even in inanimate things, since an altar, once consecrated, is not consecrated again unless it has been broken up. Consequently such a power as this remains, as to its essence, in the man who has received it by consecration, as long as he lives, even if he fall into schism or heresy: and this is proved from the fact that if he come back to the Church, he is not consecrated anew. Since, however, the lower power ought not to exercise its act, except in so far as it is moved by the higher power, as may be seen also in the physical order, it follows that such persons lose the use of their power, so that it is not lawful for them to use it. Yet if they use it, this power has its effect in sacramental acts, because therein man acts only as God's instrument, so that sacramental effects are not precluded on account of any fault whatever in the person who confers the sacrament.
On the other hand, the power of jurisdiction is that which is conferred by a mere human appointment. Such a power as this does not adhere to the recipient immovably: so that it does not remain in heretics and schismatics; and consequently they neither absolve nor excommunicate, nor grant indulgence, nor do anything of the kind, and if they do, it is invalid.
Accordingly when it is said that such like persons have no spiritual power, it is to be understood as referring either to the second power, or if it be referred to the first power, not as referring to the essence of the power, but to its lawful use.
This suffices for the Replies to the Objections.
Source: Summa Theologica (New Advent)