To be sure you have real horn, bone or ivory use the pin test. Heat a pin very hot. In an area that is not visible, touch the pin to the back. If it does not melt but burns, it is not plastic, bakelite or gutta percha.
To cut it, it is best to use a jewelers saw. This will give a fine cut. For a rougher cut, you can use a hack saw or any metal cutting blade with about 6 teeth per inch. Sanding is best done wet. You can start at 120 and move up in grades slowly. Finally it can be polished with chromium oxide or white rouge.
If the horn is beginning to crack from age or lack of humidity, you can repair or fix it to a point. The easiest method it to immerse the piece in mineral oil for a few days. Then take it out and let it dry. If time is a premium, place the piece in a pan over very low heat with mineral oil. Do not let it boil. Keep it in the heated oil for 4 to 8 hours.
To freshen any lines cut into the horn, you can use an exacto knife. Also an engravers tool will work.
Pete