one thing is sure ,don't stop your hand, follow through.
slinging(and generally throwing) is dynamic ,rifle shooting,archery, slingshot shooting etc are more static.
although im not as accurate as Jaegoor yet
i believe that aiming can be done but i have to say sling is the most difficult instrument to aim with.(If you think there is another please tell me.)
i'm thinking of writing some of my ideas on aiming with a sling but i want to write it nicely and not hastily.
for now i recommend practicing but not the kind of practice most think "i'll just throw stones around and someday it will come to me", but with intent, train your will to hit the target
try to pay attention to every little movement during the throw, fix what you think is wrong, learn what you must do to hit the target try to repeat it.
learning/training is mind over body
using the skill is body over mind (instinctive)
i recommend playing darts. it may not help you with the technique but i believe it will train your mind.
also i want to add: have you ever played pool? playing pool will show you how the mind can see what it needs to be done but the body won't listen ,very frustrating sometimes