Lots of people take up meditation and mindfulness to reduce stress. And there's nothing wrong with that; I encourage it. But the Buddha didn't teach a path of stress reduction, exactly. In fact, the concept of "stress reduction" may have puzzled him.
The idea of stress as a physiological condition was first proposed by a Hungarian endocrinologist named Hans Selye in the 1930s. Selye first defined "stress" as a non-specific response of the body to a demand for change. Nowadays we think of stress as the body's response to a "stressor," which is a situation we perceive as a threat to ourselves or our way of life.
The stressor triggers an increase in adrenaline and other bodily functions. This was useful for our ancient ancestors, who sometimes needed a burst of energy to escape from saber-tooth tigers. But the "fight or flight" response usually doesn't help us deal with the things that upset us these days. And prolonged periods of unresolved stress are detrimental to our health.
This brings us to dukkha. These days many translators and Buddhist scholars have taken to translating dukkha as "stress" instead of "suffering." Stress does seem closer to the Buddha's meaning, although I'm not sure it's an exact match.
Even so, Buddhism is not a path of dukkha reduction or dukkha management, but dukkha liberation. Further, stress relief in the therapeutic sense means achieving relaxation. Relaxation soothes our amped-up nerves and hormones and whatever else in your body is burning too hot because of a perceived threat.
In other words, stress reduction is like applying a soothing balm to a wound; dharma practice is realizing the wound is a phantasm. Buddhist practices such as meditation and mindfulness do have therapeutic applications, but stress management isn't their primary purpose.