> So you need to leave something behind in order to go somewhere?

As a definition, no. But no one has been able to figure out reactionless propulsion; as far as anyone can tell, the only way to accelerate in space is to throw something in the opposite direction (matter or light).

If you tie a rope to a hammer, then spin it around as fast as you can like a hammer thrower, and drop it. Wouldn't the breaking force propel you in the same direction your let go of the hammer?

If you're in zero g and not on a surface with friction to push against, you're not going to be able to do what a hammer thrower can do standing on Earth.

But, if you provide some momentum to an object like a hammer and release it, you will move. That goes back to "you need to leave something behind in order to go somewhere."