Depending on the source of your information, various forms of dietary recommendations have been touted to help to remove toxic waste from your body. Some regimes recommend a strict diet containing only fruit juices and vegetables while others include consumption of certain special formulation, herbs or tea. There are also some regimes which impose strict fasting with interventions such as colonic cleansing.
The issue with these recommendations is the lack of clarity on precisely what and which toxins we are targeting. Without a clear idea on the actual goal, it will be extremely difficult, if not impossible, to know if any of the recommendations actually work. If controlling weight gain and general well being are the yardsticks, any combination of exercise, calories restriction and adequate sleep and hydration may already be enough.
One important point to note is any extreme deviation from a balanced diet for a long time or methods involving invasive interventions may actually harm our body more than we know. So the version of "detox diet" I believe in is to eat in moderation, avoid drugs and excessive alcohol consumption, exercise regularly, have adequate hydration and rest and to stay happy.