If you know what kind of mold it is and are sure that it is safe to eat you don't even have to cut off the visibly discolored and changed part. Mold has long roots into the growing medium that can't be seen with the naked eye.
No, any object with mold should not be eaten, even if it is a portion of the food. That is because the organisms in the mold may have spread to other regions and may not be as visible, but still dangerous for consumption.