If you break away from someone who is trying to hold you or catch you, you free yourself and run away. I broke away from him and rushed out into the hall Willie Hamilton broke away early in the race. = cut loose
withdraw from an organization or communion; "After the break up of the Soviet Union, many republics broke away"
If you break away from something or someone that restricts you or controls you, you succeed in freeing yourself from them. Aboriginal art has finally gained recognition and broken away from being labelled as `primitive' or `exotic'