Although many Mormons don't realize it, this particular verse causes a problem with their doctrine. Let's go through, step-by-step, the root of these problems. First, it comes from their doctrine of the Trinity:
I have always declared God to be a distinct personage, Jesus Christ a separate and distinct personage from God the Father and the Holy Ghost was a distinct personage and a Spirit: and these three constitute… three Gods. (Teachings of the Prophet Joseph Smith, p. 190)
Mormons give names to the first two Personages of their Trinity: Elohim and Jehovah. To the Mormon, Elohim and Jehovah are two different gods. Elohim (God the Father) is separate from Jehovah. And who do they consider Jehovah to be? That would be Jesus in the Old Testament. See, Mormons believe that when you see the tetragrammaton (Hebrew: YHWH, or LORD in all caps) in the Old Testament, this refers to Jesus. But whenever you see the word 'God' (Hebrew: Elohim), this refers to God the Father.
I will give them this: that when you see the word YHWH, it can indeed be referring to Christ, given that He is the second person in the (Orthodox) Trinity. Colossians 1:16 says that For by Him [Christ] all things were created that are in heaven and that are on earth, visible and invisible, whether thrones or dominions or principalities or powers. All things were created through Him and for Him. When you read this in conjunction with Isaiah 44:24 (Thus says the LORD, your Redeemer, and He who formed you from the womb: “ I am the LORD, who makes all things, Who stretches out the heavens all alone, Who spreads abroad the earth by Myself...) it does point to Christ speaking in the Old Tetsament.
However, let us consider Psalm 110:1-2. The LORD said to my Lord, “Sit at My right hand, Till I make Your enemies Your footstool.” The LORD shall send the rod of Your strength out of Zion. Rule in the midst of Your enemies! In this passage, which is quoted by Jesus in Matthew 22:44, when YHWH speaks, it is the Father speaking to the son. The proper way to read this is, as David wrote, "YHWH (God the Father) said to my Lord (Jesus), 'Sit...'"
But how does the Mormon interpret this passage? Does Jesus tell Himself to sit at His own right hand? "Jehovah (Jesus) said to my Lord (Jesus), "Sit...'"?
If you are reading these passages through the eyes of an unbeliever, or someone with a skewed understanding of the Trinity, then this seems to be a contradiction. And for the Mormon, it is. However, for those of us who hold to the orthodox view of the Holy Trinity (although not always understanding it), these passages are complementary to one another.
Now, here is where the dilemma lies for the Mormon in Psalm 97:9. If YHWH, Jehovah--Jesus Christ, that is--is "exalted far above all other gods," and Elohim (God the Father) is another, separate god from Jehovah, then does this mean that Jesus is to be exalted above even God the Father?