Mob mining or ore skinning is the act of gathering ore, gems, elemental ingredients, or vendorable items from the corpse of dead giants and elementals.
To mine a dead mob, you must be at the appropriate level of mining. This is determined by multiplying the mob level by five. A level 70 mob requires a mining skill of 350 (70 x 5). A level 80 mob requires a skill of 450. Unfortunately, mining cannot be leveled in this fashion. Also, just as if you are mining a normal node, you must have a mining pick.
Eligible mobs
Only mobs of level 60 and higher can be mined. Only giants and elementals can be mined, and even then only specific kinds. According to WoWHead, there are 62 mineable mobs.
Drops
Depending on the level, mobs can drop gems of uncommon or rare quality, ore, elemental ingredients, or vendorable trash (in order of least to most frequently encountered). Mobs will only drop ore and gems from the expansion they are in. Burning Crusade mobs will not drop 
[Crystallized Life], 
[Autumn's Glow] or Cobalt, and Northrend mobs will not drop 
[Primal Shadow], 
[Crimson Spinel], or Adamantite.
See also
For more information see:
Using the same mechanic:
External links
Wowhead List of mineable mobs