If I am not mistaken (but do correct me if I am), The Church of Jesus Christ of Latter-day Saints teaches that the Father, Son, and Holy Ghost are three separate beings, i.e. three separate Gods. What Scripture passages do Latter-day Saints use to refute the “three persons in one God” view of trinitarianism?
17 It no sooner appeared than I found myself delivered from the enemy which held me bound. When the light rested upon me I saw two Personages, whose brightness and glory defy all description, standing above me in the air. One of them spake unto me, calling me by name and said, pointing to the other—This is My Beloved Son. Hear Him!
In this event, God the Father appeared as one individual introducing Jesus Christ as another separate being. There is no mention of the Holy Ghost but we can be sure he is there. (2 distinct individuals + Holy Ghost)
The Church’s first Article of Faith is:
“We believe in God, the Eternal Father, and in His Son, Jesus Christ, and in the Holy Ghost.”
(3 distinct individuals)
But he, being full of the Holy Ghost, looked up steadfastly into heaven, and saw the glory of God, and Jesus standing on the right hand of God,
Holy Ghost within Stephen, Jesus Standing next to God. (3 distinct individuals)
Then cometh Jesus from Galilee to Jordan unto John, to be baptized of him. But John forbad him, saying, I have need to be baptized of thee, and comest thou to me? And Jesus answering said unto him, Suffer it to be so now: for thus it becometh us to fulfil all righteousness. Then he suffered him. And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him: And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased.
Jesus Christ in the River Jordan, Heavenly Father's voice from Heaven, Holy Ghost descends as a dove (3 distinct individuals)
In addition to the references in Staples' answer, there is a statement in the book of Doctrine & Covenants:
The Father has a body of flesh and bones as tangible as man’s; the Son also; but the Holy Ghost has not a body of flesh and bones, but is a personage of Spirit. Were it not so, the Holy Ghost could not dwell in us.
I'd also like to reinforce that the primary reference for LDS followers is Joseph Smith's First Vision, where both the Father and the Son appear standing next to each other, recounted in Joseph Smith-History 1:17. This is the event, taken as truthful, that puts a different perspective on passages from the Bible, rather than deriving the individuality of the Godhead from prior biblical teachings.
I am a Latter Day Saint, so I can answer this. For a more fully answer, I recommend that you go to http://everyverse.org/god-triune/ (which is a site I created - feel free to comment or ask questions there to reach me). But here below are some thoughts:
FATHER AND SON HAVE/ARE SEPARATE SPIRITS: - Luke 23:26 Father, into thy hands I commend my spirit: and having said thus, he gave up the ghost/spirit. - Gen 1:2 And the Spirit of God moved upon the face of the waters - Matt. 12:18 Behold my servant… I will put my spirit upon him
FATHER AND SON HAVE/ARE SEPARATE SOULS: - Matt. 12:18 Behold my servant… in whom my soul is well pleased - John 12:27 My soul is troubled; and what shall I say? Father, save me (?)
FATHER AND SON ARE SEPARATE GODS (ONE IS THE GOD OF THE OTHER): - Ps. 45:7 God, thy God, hath anointed thee with the oil of gladness above thy fellows (compare to Heb. 1:9) - John 20:17 I ascend unto my Father, and your Father; and to my God, and your God
Hope this is helpful!