The forerunners of strategic dismemberment were early scripted encounters, most often seen during boss battles. Players would have to first disable a certain part of the boss, such as removing an armored section or chopping off a limb, in order to expose the boss's "weak spot". However, these encounters rarely involved any sort of strategic choice on the players part, but were instead necessary for the defeat of the boss, and therefore do not technically apply to this category.
While not the first to use such a mechanic, the games that coined the phrase "dynamic strategic dismemberment" were Dead Space and Dead Space: Extraction. Both games encourage players to take out adversaries by intelligently choosing portions of an opponent's body to disable. In addition, and more importantly, it is far easier to kill the Necromorph enemies in Dead Space by blasting off their limbs than it is to kill them by simply shooting them in the torso.
This page is dedicated to games where specifically targeting and removing the limbs of the player's enemies is a centrally valid strategy that results in the enemy no longer being able to use certain tactics against the player. For the list of any game where bodies can be rent asunder, see: Dismemberment.