What is the ruling on killing animals in a painful manner by dismembering them by hand in some military training?

The basic principle is that it is impermissible to torture an animal without a legitimate Shariah purpose. The Lawgiver (Allah) commanded showing kindness to everything, even animals, and forbade taking any living creature as a target. What you mentioned about training does not constitute a valid reason for killing animals in the manner described, due to the torture inflicted upon creatures whose torture has been prohibited, especially since other training methods exist.