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.
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.
For more information see: