Spiritual Death

15 For behold, he surely must die that salvation may come; yea, it behooveth him and becometh expedient that he dieth, to bring to pass the resurrection of the dead, that thereby men may be brought into the presence of the Lord.
16 Yea, behold, this death bringeth to pass the resurrection, and redeemeth all mankind from the first death—that spiritual death; for all mankind, by the fall of Adam being cut off from the presence of the Lord, are considered as dead, both as to things temporal and to things spiritual. (Helaman 14)

11 And because of the way of deliverance of our God, the Holy One of Israel, this death, of which I have spoken, which is the temporal, shall deliver up its dead; which death is the grave.
12 And this death of which I have spoken, which is the spiritual death, shall deliver up its dead; which spiritual death is hell; wherefore, death and hell must deliver up their dead, and hell must deliver up its captive spirits, and the grave must deliver up its captive bodies, and the bodies and the spirits of men will be restored one to the other; and it is by the power of the resurrection of the Holy One of Israel. (2 Nephi 9)

16 And now behold, I say unto you then cometh a death, even a second death, which is a spiritual death; then is a time that whosoever dieth in his sins, as to a temporal death, shall also die a spiritual death; yea, he shall die as to things pertaining unto righteousness.
17 Then is the time when their torments shall be as a lake of fire and brimstone, whose flame ascendeth up forever and ever; and then is the time that they shall be chained down to an everlasting destruction, according to the power and captivity of Satan, he having subjected them according to his will.
18 Then, I say unto you, they shall be as though there had been no redemption made; for they cannot be redeemed according to God’s justice; and they cannot die, seeing there is no more corruption. (Alma 12)

5 For behold, if Adam had put forth his hand immediately, and partaken of the tree of life, he would have lived forever, according to the word of God, having no space for repentance; yea, and also the word of God would have been void, and the great plan of salvation would have been frustrated.
6 But behold, it was appointed unto man to die—therefore, as they were cut off from the tree of life they should be cut off from the face of the earth—and man became lost forever, yea, they became fallen man.
7 And now, ye see by this that our first parents were cut off both temporally and spiritually from the presence of the Lord; and thus we see they became subjects to follow after their own will.
8 Now behold, it was not expedient that man should be reclaimed from this temporal death, for that would destroy the great plan of happiness.
9 Therefore, as the soul could never die, and the fall had brought upon all mankind a spiritual death as well as a temporal, that is, they were cut off from the presence of the Lord, it was expedient that mankind should be reclaimed from this spiritual death.
10 Therefore, as they had become carnal, sensual, and devilish, by nature, this probationary state became a state for them to prepare; it became a preparatory state. (Alma 42)

Physical Death

11 Now, concerning the state of the soul between death and the resurrection—Behold, it has been made known unto me by an angel, that the spirits of all men, as soon as they are departed from this mortal body, yea, the spirits of all men, whether they be good or evil, are taken home to that God who gave them life.
12 And then shall it come to pass, that the spirits of those who are righteous are received into a state of happiness, which is called paradise, a state of rest, a state of peace, where they shall rest from all their troubles and from all care, and sorrow.
13 And then shall it come to pass, that the spirits of the wicked, yea, who are evil—for behold, they have no part nor portion of the Spirit of the Lord; for behold, they chose evil works rather than good; therefore the spirit of the devil did enter into them, and take possession of their house—and these shall be cast out into outer darkness; there shall be weeping, and wailing, and gnashing of teeth, and this because of their own iniquity, being led captive by the will of the devil.
14 Now this is the state of the souls of the wicked, yea, in darkness, and a state of awful, fearful looking for the fiery indignation of the wrath of God upon them; thus they remain in this state, as well as the righteous in paradise, until the time of their resurrection. (Alma 40)