Somehow I have been using mindfulness techniques since puberty. Works well, when it is about dealing with pain for me. I can discern between pain to act on, and pain to just let be till it passes.
When it comes to stress, I have used the same techniques to endure more than I should have. Finally learning to discern between stress that will pass, and stress that needs action to prevent mental havoc.
When taught properly, not only should the techniques learn you how to deal with stress in a way that it will not bother you that much, but also that it will make you act, when action is needed.
If taught well, your boss should also get critique on things that lead to things structurally leading to unnecessary stress.