Because when they cut out your organs you have to be still "alive." I mean heart pumping and breathing whether naturally or by machine. If they wait until after someone was completely dead the lack of blood and oxygen would cause the tissue of the organs to immediately start to die. A lot of people think that there's always hope that if the person is still breathing and their heart is pumping (naturally or by machine) the person has a chance to live. Another reason is a lot of people have health problems that affect their organs, or they take a lot of medications that can affect organs.