When one of your soldiers has picked up a lying body in Third Person (Drone) view, the Drop Body button appears next to the Grenade button. Tap and hold the Drop Body indicator, dragging it to where you want to drop the body. When you release your finger/thumb from the screen, your soldier with the body will move to that location and drop the body.

To cancel dropping a body in Third Person (Drone) view, drag the indicator off the screen or to an invalid location. You can also switch to First Person view and the soldier will automatically drop the body he is carrying.