When you are dead the life processes in your body cease.

Sure. Eventually. As you say, life processes plural. Different parts of the body die at different rates as the processes shut down and stop at different rates. The heart will keep beating so long as there is a machine keeping the lungs pumping.

Theologically speaking, death is when the soul leaves the body.

So animals, plants and bacteria are dead because they don't have souls? How about skin cells? Does every skin cell have a soul? Is that the same soul as your red blood cells and the cells of your liver? Or do they never die?

Let's keep this discussion about reality, not made up fiction.

You’re gonna die someday, can we take your organs now?

Depends. If you are somebody I care about, I might donate a kidney. If I'm brain dead, being kept artificially alive by a pump, with no brain activity and no hope of recovery, then sure. Waste not, want not.

Why would I want to take up a space on a respirator, waiting for infection to shut down my lungs and heart, just to keep a chunk of meat going, when there are people with genuine chance of recovery who could be saved?