• Carbon di Oxide Process: In this process, already steamed coffee beans are either soaked (technically speaking, subjected to) in liquid Carbon di oxide (CO2 gas under high pressure liquefies) or Carbon di Oxide is passed at high pressure through water containing soaked beans and subjected to carbon (charcoal) filters. This method can be called organic because Carbon di Oxide is considered an organic gas (even if produced synthetically) scientifically. So, you can go ahead with this.
• Coffee Oil (Triglyceride) Process: In this process, the coffee beans are first soaked in hot water (some caffeine is removed first hand), removed, and then soaked in coffee oil. The triglycerides present in coffee oil pull out the caffeine from the surface of the beans (the caffeine surfaces due to action of hot water). Thereafter, the beans are removed and dried. This method preserves the flavour and the taste of coffee to a great extent. The oil left can be reused after removal of the caffeine from it. This method of removal of caffeine from the oil before reusing is what decides whether the coffee can be called organic or inorganic. If the oil is decaffeinated using chemicals (Methylene Chloride etc.), then it is no more organic. If some organic method like charcoal filters is applied for this purpose, then it can be called organic.
Why Decaffeination? Caffeine is an external stimulating agent and can be harmful to health in the long run and in overdose. It can give birth to serious troubles like chronic headache, chronic fatigue, annoyance, lungs disorders, high blood pressure, nervous disorders, anxiety, insomnia, lack of appetite etc. Caffeine found in coffee is much higher than that in tea and hence it becomes important to decaffeinate it. Decaffeinated coffee lets you enjoy the remarkable flavour and taste of coffee without risking your health.