Removing part or whole exhaust system from car will enhance performance up to a point. an engine is nothing more than an air pump. most factory exhaust sytem are too restrictive, thus prevent exhaust from engine exiting fast enough. but, engines are design to have some back pressure to suck some exhaust back into engine to warm up incoming intake gas mixture to better combustion.
In the end, what you need is a good aftermarket replacement exhaust system design for performance.