The counterweight orbits above escape velocity, pulling the space elevator's cable taut. If the cable were severed the counterweight would drift off into space into a solar orbit. So if you jump off at the counterweight, you'll enter solar orbit.
At geostationary orbit (which could be considered the "top" of the space elevator as that's where you would normally get off, presumably) the space elevator orbits at exactly orbital velocity, so if you jump off there you end up in orbit. Below that your velocity would be below orbital velocity and you'd fall back to Earth.