That’s a darn good question. For those of you who don’t know, “A revision or translation of the King James Version of the Bible begun by the Prophet Joseph Smith in June 1830. He was divinely commissioned to make the translation and regarded it as “a branch of his calling” as a prophet. Although the major portion of the work was completed by July 1833, he continued to make modifications while preparing a manuscript for the press until his death in 1844, and it is possible that some additional modifications would have been made had he lived to publish the entire work. Some parts of the translation were published during his lifetime.” (from http://lds.org/scriptures/bd/joseph-smith-translation?lang=eng).
So why don’t Mormons use this Joseph Smith Translation of the Bible (JST, for future reference)?
Perhaps the biggest reason is that it was never really finished, per se, prior to Joseph’s death. The normal path for it to be accepted as scripture by the LDS Church would have been for it to be finished, approved officially by the leadership and membership of the Church, and then and only then would it have become scripture for the LDS Church. But Joseph was killed while still working on it. After that, his wife Emma left the LDS Church and retained possession of the original manuscripts, so the LDS Church didn’t even have the JST. After Brigham Young took the members west to present-day Utah, there was a lot of mistrust between the Reorganized Church of Jesus Christ of Latter-day Saints, founded with Joseph and Emma’s son as its leader, and the LDS Church. Brigham Young and others suspected the RLDS Church had tampered with the original manuscripts. It wasn’t until the early 1970s that the RLDS and LDS Churches began to cooperate on certain matters and the JST started being used as a reference in the LDS Church. At this point there was well over 100 years of the King James Version being the standard Bible for Mormons, and so in 1980 a revised version of the KJV Bible was printed with footnotes and references to the JST, with some parts of the JST having been canonized.