It never specifies in the Doctrine and Covenants Section 89, Why we are discouraged from drinking "hot drinks" which Joseph Smith later clarified as "tea and coffee." 
 
It's not because of the caffeine.  
 
I really think it's because God told us not to. Just like the Jews can't eat certain meats unless they are prepared a certain way. Is it because they are bad for them? No. It's cuz they believe that God told them not to. It's along those same lines.  
 
The Church of Jesus Christ of Latter-Day saints has never issued a statement "officially," discouraging the drinking of drinks that contain caffeine. They do offically discourage drinking tea and coffee.

Caffeine is not prohibited in the writing of the Words of Wisdom. The actual prohibition is on hot drinks, aka Coffee and Tea.  
 
Now while caffeine is a addictive drug in coffee and tea, the ban is on coffee and tea not caffeine.  
 
Recent prophets do warn against using caffeine, understanding that it is an addictive drug and the intention of the Word of Wisdom was to protect the Saints from such addictive and harmful drugs. But there has never been any revelation that explicitly prohibits caffeine, though it is implied in the Word of Wisdom.  
 
Many Mormons (myself included) choose to not partake of caffeinated beverages understanding that the Word of Wisdom warns against all harmful beverages not just tea, coffee, and alcohol.  
 
This is a decision to be made individually though and unless further revelation is received it will stay that way.  
 
It is also important to note that obedience to the Word of Wisdom is not a requirement to be a active member of the Church. It is required to become a member and to receive callings and be able to enter the temple, but there are plenty of LDS members that struggle with addiction to alcohol, tobacco, coffee, and tea.  
 
They are loved and supported by there congregations as they work to overcome these addictions and become free of the destructive path of addiction!

The Church does discourage the use of any addictive substances this includes caffeine. The Apostle have discussed this and council us to avoid all non medicinal drugs so they do officially discourage the use of caffeine.  
 
In fact Brigham Young University (an LDS College in Provo, Utah) has a ban on all caffeinated beverages.  
 
The use of caffeine is officially strongly discouraged but not prohibited (with the obvious exception of coffee and tea). 
 
For more information of the LDS views on addictive drug like caffeine please feel welcome to look at www.lds.org and www.mormon.org 
 
Both of these sites have a mountain of information about our doctrine and policies!