Excommunication does not remove priesthood. When excommunicated the church requests that priesthood not be used during the period of exclusion from church membership. But priesthood itself is not and cannot be removed by an excommunication proceeding.
Priesthood can and is removed by God. He removes it when men who have been ordained use their authority to “cover [their] sins, or to gratify [their] pride, [their] vain ambition, or to exercise control or dominion or compulsion upon the souls of the children of men” at which point “behold, the heavens withdraw themselves; the Spirit of the Lord is grieved; and when it is withdrawn, Amen to the priesthood or the authority of that man.” (D&C 121: 37.)
So if a man has not lied, nor cheated, nor committed adultery, nor violated his covenants with God, but is excommunicated because he thinks something the church does not want him to think, it is possible priesthood may be forfeited if this man is excommunicated, but this would not be the man targeted for excommunication. Such a church court would exercise the control, the compulsion, and the dominion against the man. He is not and cannot be responsible for wrongly using priesthood to control another, for he is not seeking to force others to think like he does.
If, therefore, excommunication affects priesthood, the way that would manifest itself is in the members of the court/council forfeiting their priesthood by their wrongful acts. Similarly, other priesthood authorities who participated, encouraged, ratified and sustained the court’s wrongful deed would share in the responsibility and be similarly responsible for the abuse.
In every case of excommunication, the one on trial is not regarded by the church as losing their priesthood. They are instead requested to temporarily stop using it. Inside the church itself, they are not permitted to use it. But it is up to the individual to decide whether or not to use it in other circumstances. Before annotations were made to church membership records, the way excommunication was apparent was by comparing the date of baptism to the date of ordination. If a member had been ordained before their baptism, then it was apparent they had been excommunicated.
Orson Pratt was ordained an Apostle as one of the original Twelve on April 26, 1835. He was excommunicated August 20, 1842. He was reinstated on January 20, 1843. He was never re-ordained an Apostle when reinstated. However, his “seniority” in the Quorum of the Twelve was reckoned from the date of his readmission in January 1843 and therefore he moved down in seniority and Brigham Young became his senior.
Every other Apostle who was excommunicated was similarly readmitted without being re-ordained.
No one is re-ordained when re-baptized. Their original ordination stands.
Excommunicants are only requested to not use their priesthood. But they still possess it.