Yes, as our 8th Article of Faith states we believe the Bible is the word of God as far as it is correctly translated. What this means is that since the Bible was compiled and canonized under the commission of a Pagan Emperor to gain political power for his newly created state religion.  
 
We know that many epistles and gospels were excluded from the New Testament at the Carthaginian Convention so the New Testament is incomplete, we also know from scripture study that there are books referenced in the New and Old Testament that we do not have once again showing that the Bible has missing parts.  
 
There actually is a Mormon translation of the Bible, it is called the Joseph Smith Translation and it is the inspired translation of the King James Version of the Bible. It provides has many corrections and lost passages restored to the KJV. The Joseph Smith Translation is found in the footnotes of every LDS edition of the KJV Bible.  
 
The reason why the LDS Church does not have an edition of the Bible with the lost books restored to it is because those books were either lost thousands of years ago or still currently sit in a locked private vault in the Vatican with only a powerful few being able to access the documents.  
 
Without the manuscripts it is impossible to have a translation of the documents, we know that in time all the lost manuscripts will be restored, much of this restoration will likely happen during the millennial reign of Christ though.  
 
Hope my answer helped!

The Book of Mormon contains a great explanation of this doctrine in 1 Nephi 13. 
 
Here the prophet Nephi has a vision in which he sees the record of the Jews (now known as the Bible) which originally contained the fulness of the Gospel of Jesus Christ pass through the hands of a "Great and Abominable Church" founded by the devil. (This Great and Abominable church is not any specific church, rather it is essentially the world or worldly organizations in general) 
When this book passes through the hands of this "church", many of the plain and precious truths and many of the covenants of the Lord are taken away and lost. Because of this, many people stumble and walk in blindness and Satan gains great power over them. 
Nephi also sees, however, that God has prepared a great and marvelous work in the last days. He reveals to Nephi that He will manifest himself unto Nephi's descendants and that they will write of His teaching and ministerings and that these writing will come forth in the last days (as the Book of Mormon) to establish the truth of the first (the Bible) and restore the plain and precious truths that were lost and that the two of them would become established in one and demonstrate that "there is one God and one Shepherd over all the earth." 
Although Joseph Smith did create a translation to the Bible (the word "translation" used loosely because it was not a translation from ancient manuscripts but rather a restoration through the power of revelation), it was not intended to be a replacement for the King James version of the Bible that we had. Rather it seems to have been more of an instructional tool for Joseph, for it was during this "translation" time that Joseph received many of the revelations regarding the restoration of the Church. The "plain and precious truths", however, were really restored through the coming forth of the Book of Mormon and in the many revelations that comprise the Doctrine and Covenants. God didn't need to restore all of the lost parts of the Bible. He had another, even better, plan all along.

Thank you guys for answering that question. That makes more sense now. 
 
Now I just have one more question. Maybe I should just post a new one, but I'll do that if no one answers this. 
 
So my question is: Why is it believed that the Bible is not the only "book". If you can understand what I'm trying to ask? 
 
I'm just confused because the Bible says that nothing should be added to it. I hope I didn't word that weird. 
 
I'm sorry if I plague this site with questions. I'm just curious to figure out these things.

I have yet to find any scripture that states that God stopped communicating with his Prophets at Revelations.  
 
There are two closed Books in the Bible, Revelations and Deuteronomy there is no other closed books int he Bible, in fact if there was any verse that states that there will be nothing added or subtracted to "The Bible" I would state that is an addition to the scriptures since the Bible as we know it was created almost 400 years after the last writings of any of the New Testament Prophets.  
 
During the time of the Apostles there was no central volume called a Bible, the Bible was compiled in the 5th Century AD.  
 
Many hold this belief that the Cannon is closed after Revelations, that God stopped communicating with the World and that is not the truth of the scriptures though, IMO.  
 
We are told that the Church is built upon a foundation of Prophets and Apostles, that they are needed to unify and perfect the Saints and to remove false doctrine from the truth of the Gospel.  
 
As long as we have living Apostles and Prophets we will always have new revelations and scriptures as the Lord reveals his secret through his servants the prophets.

Sam, 
 
Your last question is one of the easiest to answer. Here are a raft of resources about it: http://www.fairlds.org/apol/ai104.html

At the time these verses were written, there was no "Bible" they were individual books that were compiled later. So that means that those verses only referred to the books that they existed in at the time they were written, namely Revelations and Deuteronomy.