When the amygdala (our alarm system) recognises danger it sets the sympathetic nervous system off which also mediates much of our automatic fight or flight responses, what we often describe as stress.
We have no direct conscious control over our amygdala, it’s a one way messaging system, apart from breathing (afaik). Breathing is one of the few ANS controlled functions that we have conscious control over.
In breathing slowly and deeply we decrease the rate we’re firing the sympathetic nervous system and increasing the rate of firing of the parasympathetic nervous system (muscles contract once, muscles relax for extended period).
I suspect this actually allows us some level of communication with the amygdala, perhaps allowing us to turn it off, or reduce it’s volume, which in turn would reduce the level of stress we experienced.