How to turn an outdoors tree stump into a table?
It will rot.  Eventually.  However, there's no reason why you can't enjoy it as a table for many years.  I'd smooth off the surface after it dries a bit and seal it with a deck sealer.  This will help preserve the top.  But it will continue to rot from below, and eventually you'll have to remove it.  

How long from now "eventually" actually is is dependent on many factors such as climate, exposure, type of wood, animal and insect presence.