The crossover (at 600hz) will decrease the volume of the driver gradually (the slope) so that the mid-range speaker will take over and produce the sound until it hits the next crossover for the tweeter. So the crossover creates a downward slope for the driver and an upward slope for the mid, that sort of intersects at the crossover point.
The driver will still be producing some sound at 700hz and 800hz and above, but it will be reduced by 6,12,18,or 24db per octave, depending on the degree of the slope. The reverse is true of the mid. It might start out at 300hz and be 24db down. It will gradually get louder until around the 600hz mark, where hopefully it will blend perfectly with the driver. Such is the plight of the speaker builders!
The crossover doesn't "deliver" from 30-600, but it does slow down and stop the speakers from delivering above and below that point. Hope this helps a bit!