To take the horn off your unicorn, you have to go to the bottom right of your unicorn's page. You should see a box like the one pictured on the right. Click remove, and your unicorn will become a regular horse, and you will now have a new ingredient.
Warning: If you remove the horn from a unicorn, you will never be able to get it back. Removing the horn from a Golden Apple unicorn results in the loss of the GA coat plus the bonuses from the GA. You will only be able to get the GA back by purchasing another one.
The only other way to obtain the Unicorn Horn ingredient is to pay a large price for them at the flash sales. The event lasted from 27th May 2013 to 13th June 2013.