Removing a rusty or corroded screw without breaking it off can be tricky, but it's not impossible. All it takes is some lubricant, a few sharp blows, and a lot of finesse.
Next, use a rust penetrant like WD-40 Specialist Rust Release to lubricate the screw head and threads. Rap it a few more times, then let the lube penetrate for about 15 minutes.
Strike the head a few more times, then try to remove it with a screwdriver. If necessary, use duct tape on the end of the screw head to get the grip needed to pull it loose.
Another method is to hold a small torch at the screw head for about 5-15 seconds, letting the expansion and contraction from the heat break the bond. When cool, try unscrewing it.