The Mormon church explains its dogma of an ordained ministerial priesthood after the order of Melchizedek and its secondary Aaronic priesthood as follows:
“There are, in the church, two priesthoods, namely, the Melchizedek and Aaronic, including the Levitical Priesthood. Why the first is called the Melchizedek Priesthood is because Melchizedek was such a great high priest. Before his day it was called the Holy Priesthood, after the Order of the Son of God. But out of respect or reverence to the name of the Supreme Being, to avoid the too frequent repetition of his name, they, the church, in ancient days, called that priesthood after Melchizedek, or the Melchizedek Priesthood. All other authorities or offices in the church are appendages to this priesthood. … The second priesthood is called the Priesthood of Aaron, because it was conferred upon Aaron and his seed, throughout all their generations. Why it is called the lesser priesthood is because it is an appendage to the greater, or the Melchizedek Priesthood, and has power in administering outward ordinances.” (Doctrine and Covenants 107:1–5, 13–14)
Melchizedek, whose name literally means king of peace and righteousness, was a distinct kind of priest who directs our attention to the perfect, unique priesthood of Jesus Christ. The position of High Priest is exclusively reserved for Christ. His priesthood, which is of Melchizedek's priestly descent, is superior to the Levitical priesthood because it is eternal (Hebrews 7:11-12; 23-25). Jesus Christ forever lives to make intercession for those who approach Him. This source
says the following about the meaning of the word "unchangeable" found in Hebrews 7:24:
"The key word is “unchangeable” (aparabatos), which suggests that the Lord’s priesthood is imperishable. Some suggest that the meaning of the Greek term is simply “permanent, unchangeable” (F.W. Danker, et al., A Greek-English Lexicon of the New Testament, Chicago: University of Chicago, 2000, p. 97), which, of itself, would eliminate the Mormon idea. But even more to the point is the proposed meaning “non-transferable” (C. Spiqu, Theological Lexicon of the New Testament, Peabody, MA: Hendrickson, 1994, 1.143-44). That would specifically deny that it could pass to other persons."
Thus, the Mormon church's claim to possessing a priesthood after the order of Melchizedek has been fabricated out of thin air. It has not been sanctioned by God. Men have arrogated for themselves a position that only Christ can take on.
The Old Testament records the role of priest belonging exclusively to members of the Tribe of Levi (Numbers 18:1-7; Leviticus 6:19-23; Nehemiah 7:61-65). The majority of Mormons, along with Joseph Smith, have asserted that they are descendants of the Tribe of Ephraim. It would follow that most Mormon priests in the "Aaronic" role are under the wrath of God because they have assumed a position that does not belong to them but to the Levites (Numbers 16:1-14; 1 Kings 13:33-34). The House of Ephraim has no rightful claim to the priesthood.
The priesthood of Melchizedek is held by Jesus Christ Himself. His eternal priesthood has put an end to the ordained ministerial priesthood (Hebrews 7:11-12; 8:6-7). The Bible nowhere speaks of a distinguished hierarchy of priests who preside in accordance with Melchizedek. In fact, this ruling male figure is mentioned only twice in the Old Testament as he blessed Abraham (Genesis 14) and in a Messianic Psalm (Psalm 110). The higher order of priesthood in Mormonism has been rendered of no authority.
Exodus 29:4-27 lists certain rituals that one must perform in order to qualify as a Levitical priest. The Mormon priesthood does not offer blood sacrifices and follow various temple ceremonies as prescribed by the Law. So the "Aaronic" priesthood of Mormonism has been shown to be a fraud.
Furthermore, the assertion that Mormons have been conferred with an Aaronic priesthood is refuted because that ministerial office has been fulfilled by the Cross. Jesus Christ is the only way in which man in his sinful condition can come near to God. The tearing of the veil in the temple signifies the termination of the Lord dwelling in tabernacles made with human hands (Matthew 27:51-54). The type of priesthood set forth by the New Testament is the priesthood of all believers (1 Peter 2:5-9; Revelation 1:5-6).
The priesthood that was operative during the Old Testament was kept specially for Aaron and offspring within the tribe of Levi (Numbers 3:6). That would disqualify the Mormon priesthood because it contains Gentiles.
"Researchers who have closely examined the D&C and primary source accounts found that the official narrative of priesthood restoration contains numerous gaps, inconsistencies, and contradictions. Scholars also raise important questions that expose potential weaknesses in Smith and Cowdery's story of their miraculous ordinations. For example, if Joseph and Oliver had experienced events as remarkable and life-altering as divine visitations by John the Baptist and three of Christ's apostles, why would they not tell others? These miraculous ordinations were not publicly revealed or documented until five years after they supposedly occurred. Moreover, if the restoration of the priesthood is a fundamental tenet of the LDS Church, why was this revelation excluded from the Book of Commandments when it was originally published in 1833, only revealed in the revised and re-named Doctrine and Covenants in 1835?" (http://www.mormonthink.com/priesthood.htm#ref4)