Taxidermists sometimes will make a cast of the same point/horn on the opposite side. Once it is made they cut away the damaged area and make the surface flush. Then it is a simple matter to drill holes in the base of the area where it is cut off and the base of the cast and glue a pin of the proper size in place. They then fill in the area around the seam with what is basically bondo and stain the area to match the original antler/horn. If they do the job right you literally can't tell the difference.

I once shot a Vaal Rhebok in South Africa that was missing about 4 inches off one horn from an old break and the above is exactly how they repaired it. I had the animal done life size and unless you look very closely from exactly the right angle you can't see the repair. If the light hits it exactly right you can see a very small area where the surface texture is different and that is all but the way the mount is displayed that side it towards the wall anyway.