Deep breathing is a form of overbreathing and won’t help you at all. Oxygen requires a certain amount of carbon dioxide to be utilised, and breathing too much ironically leads to oxygen deficiency. Relatively short inhalations with extended exhalations will produce the effects you’re after.
Proper breathing massages your organs and aids the muscular contractions of your gut (peristalsis). It also improves circulation, including that of the lymph system, which is probably where the detox aspect comes in. Longer exhalations will activate your parasympathetic nervous system (responsible for “rest and digest” functions), which will help you overcome stress.
If nothing else, you really need to learn to breath through your nose. Mouth breathing leads to air being swallowed, which can lead to bloating in the intestines. It’s hard to control the rhythm through your mouth too, especially while sleeping. I found the Butekyo Method easy to follow, but I never managed to do it while sleeping until starting the diet, when my sinuses cleared up. Try reading this and this.