Mitochondria are responsible for the production of the majority of the cell's energy in form of ATP. The process requires oxygen and thus it is called cellular respiration. It is a very effective process that produces 38 ATP molecules per oxidized glucose molecule.
The lack of mitochondria in the body would have the same result as the lack of oxygen: anaerobic respiration. This type of energy production is very ineffective and it results in only two ATP molecules. Thus, if people would loose their mitochondria, they would not survive for very long as anaerobic respiration does not produce enough cellular energy.
Furthermore, anaerobic respiration also has a detrimental side effect: lactic acid. This chemical substance results during the conversion of glucose into ATP. Its presence and accumulation increases the acidity in muscle cells and is responsible for the "burning" sensation after intense physical activity.
In order to remove the lactic acid, it is required the action of primarily the liver and kidneys as well as skeletal muscles to a lesser degree.
In conclusion, a person would not be able to survive for very long without mitochondria. Anaerobic respiration is meant to supplement cellular respiration for only short periods of time and not replace it.
