If your aloe vera plant has dried or browning leaves it may be sunburnt or just lacking enough moisture in the soil.
If you normally keep the plant in direct sunlight, relocate the plant to a more central portion of the room.
Water your aloe vera deeply (about 1 to 2 inches of water a time) but infrequently, about once a week. Ensure that the soil dries out between waterings. If you have overwatered the plant, drain out excess water, and consider repotting it in fresh soil.
Once cut, that portion of the aloe vera plant will not regenerate. Don't be afraid to cut away brown areas though, as it allows the plant to focus energies on other areas.