The Alternator belt of the car is damaged and start to break I just notice it because of a noise the engine was doing, When I checked I notice that a piece of the belt was touching a pipe, I try to cut the piece and when I started the engine the noise restarted, is like if the belt is pealing on one side.
Would I damage the car if I drove it to the mechanic that is 30 miles away from were I leave?
You can drive the car that way as long as you are aware of what can happen if the belt breaks. If all it runs is the generator you can keep on driving for about a half hour before the battery will run down. Don't stop the engine because it may not restart. Your mechanic will recharge the battery if necessary.
If the belt also runs the water pump the engine will overheat if the belt breaks. As long as the battery holds out you can drive about a mile, coast to a stop, turn the engine off and let it cool down for about 20 minutes. Then you can restart it and drive another mile, coast, and let it cool down again. Don't let it overheat as that can lead to expensive repairs.
If that belt runs the power steering pump you will have to work at turning the steering wheel at low speeds. On the highway you'll barely notice it's not working. In some cases power steering fluid will dump out of the reservoir. That is not uncommon or harmful, other than the mess it makes, and you can refill it later.