What would happen if a planet is removed from the solar system?
This question isn't really very clear or practical. You need to add quite a bit of information, eg which planet? 


If Sedna vanished, it would be detectable by instruments, but we would not notice. 
Jupiter or Mars might make a bigger difference. We could spot it straight away by the naked eye. 


Of course Earth life would be fine at first (unless it was Earth that was removed ...) but the orbits of asteroids and other bodies may be perturbed, which could lead to an influx of asteroid strikes - potentially - in the longer term.