While the clinical term "sex addiction" is a controversial one, clinical experience clearly shows that some individuals struggle with regulating their sexual behaviors. They engage in behaviors that are either contrary to their core values, high risk, harmful to self or others, distressing, or disruptive to their lives. It would be foolish to argue that sex behaviors should never be self-regulated in any way, just as we would never argue all eating, gambling, or exercising behaviors are inherently healthy.
Sexuality, however, is an aspect of self essential to the human experience. It is not healthy to respond to sexual thoughts or urges with a blanket label of "bad," and try to control them through various means of suppression. The 'sex addict' does not need to eliminate their sexuality, rather they need to develop a healthy sexuality that is congruent with their core values.
This is where mindfulness comes in. A common definition of mindfulness - "paying attention, on purpose, to the present moment, with a nonjudgmental attitude." The person struggling with dysregulated behaviors needs to learn how to experience sexual thoughts and urges without either suppressing them or engaging in unhealthy behaviors. Mindfulness can help cultivate this new response that does not see the thoughts/urges as "bad," but also does not get hooked by them. There are two regular practices to develop a new response pattern.
Sitting meditation. The core of many traditional and clinical mindfulness practices. You can find many free guided mindfulness of breath meditations online. Practice sitting quietly, directing your attention to the experience of breathing. Each time you notice that your mind has wandered, congratulate yourself, and gently guide your attention back to your breath. Do this non-judgmentally. Start with five minutes and gradually increase your time. This practice teaches awareness of inner experiences (such as the constant flow of thoughts), while increasing our ability to disentangle ourselves from thoughts without seeing them as 'bad.'
Applied mindfulness in the moment. Here, I pull from ACT (Acceptance and Commitment Therapy) cognitive defusion processes. When a sexual thought or urge arises during the day, instead of fighting it or suppressing it, try responding with "I'm having the thought/urge...(fill in the blank). I notice myself having the thought/urge...(fill in the blank)." If the thought/urge continues to linger, try engaging mindful breathing (explained above), becoming curious and aware of this internal experience, allowing it to linger or pass on its own.