CO2 acts on fires in two ways: The release of the gas under pressure has a cooling effect, as can be seen by the resulting mist cloud and ice particles; the gas also displaces the oxygen that's necessary to maintain combustion.

These are the reasons behind the uses of the co2 in fire extinguisher.

But the co2 is not directly used in the extinguisher

In the inner part of the extinguisher, the whole container is filled with the strong solution of sodium carbonate. And there is a glass tube in the bottom of the container contains sulfuric acid. The glass tube is broken with a powerful pressure when required. And the solutions are reacted with each other and carbon dioxide is produced. Then the co2 is released through the tiny hole in a very high pressure and extinguishes the fire.

Na2CO3 + H2SO4 > Na2SO4 + H2O +CO2

But the fire causes by the magnesium can't be extinguished by co2

Because…. when magnesium burns Heavy heat is generated. In the heavy heat the co2 resolved in oxygen and carbon. So in the contact of the oxygen, Magnesium burns even better and instead of extinguishing, the fire increases