The dismembered mesh/limb must be weight painted 100% in its respective bone. To ensure this, you may have to delete all other vertex groups from the “gibbed” mesh/limb. For example, in Blender, if you want to dismember a left forearm, go to edit mode, select all faces of the left forearm, press “Y” and assign 100% to the vertex group of the left forearm bone. Now, if you go to Weight paint mode, the entire left arm will be red (no green, yellow, light blue etc which causes the stretching).