Don't sweat it if you have to use the full tablet; just blow it out. A good puff will kill it. The tablet will give off a white, smelly smoke when you do this, but have a scrap of aluminum foil handy to put around the hot tablet to stop it from smoking. The smoke is actually hexamine, and the part that condenses on the inside of the foil is still good fuel - just thin flakes. They light very quickly, and if you shake them off onto the cooled remainder of the tablet, they will make your next start easier.
It is very hard to get uniform pieces when breaking or cutting Esbit. If anyone knows something that is really effective (no guessin, please) let us know. Otherwise, blowing it out is probably the better method.
Too bad the supply of military surplus hexamine has dried up. The mil tablets were about 0.2 oz. and worked fine for a cup of water.