Generally, there are two parts that can break or be damaged – the wheel and the barrel.
If the wheel is damaged or worn, you can replace the head. When considering that, look at the cost of the head and consider whether the small cost difference indicates you should buy a new cutter instead.
The most common damage is a flat spot on the wheel. You can check for this, immediately after dropping the cutter, by lightly moving the cutter across a smooth piece of glass. If you hear a regular ticking sound, the wheel is probably “flat spotted” and will need to be replaced.
A worn wheel is more difficult to detect and is also much less likely to occur. I have been using some of my cutters for 15 years without any sign of being worn.
Sometimes the plastic barrel cracks or breaks. This will mean that the oil in the cutter will leak out. So you can consider continuing to use the cutter without oil, or by dipping the head in an oil soaked bit of cotton wool or similar material before each cut.
If the break is at the threaded end and you want to continue to use the ball at the end for tapping purposes, you can glue the barrel back together with an epoxy resin. Make sure the pieces are free from oil. Then glue and allow to cure. After curing, sand down any excess resin to make the cutter comfortable to handle.
Then for additional strength you can wrap with dental floss or extremely fine wire. Start below the glued area and go to the end of the break and back again. You could coat this wrapping with epoxy again both to secure the wrapping and to further increase the strength.
Another solution is to cut the cracked end off and re-thread the remainder. It makes the cutter a little shorter, but will continue to hold oil and give good service.
Or, you could buy another cutter.