Giant mites drop out of trees occasionally when a dwarf starts cutting it down. Even on the highest difficulty setting, a giant mite is no thread for even an unarmed dwarf. Your best chance is to do it on the forest world right in the beginning (campaign or free game). Manually control a dwarf without any armor on and cut trees down until a mite spawns. Stay in manual control and simply do nothing until the mite killed your dwarf.