Ayurveda recommends the appraoch of vomiting to clear out toxins from the stomach, but it is a little extreme for my taste and that of others. It has been used successfully, though, for thousands of years.
Chewing food 30 times each bite is an indirect way of cleansing the stomach. The enzymes produced by the salivary glands while masticating the food don't just digest carbohydrates but also cleanse the stomach and keep it clean. Taking sips of hot, ionized water (see the books) also helps to break down toxins in the stomach.
And, yes, besides taking care of the above as well as diet and lifestyle, colon, kidney and liver flushing are important for the digestion to improve.