Cutting a bar magnet in two pieces produces?

Magnetic materials are notoriously hard so you will damage an ordinary hacksaw blade if you cit a bar magnet with a hacksaw (but you should eventually succeed if you do not mind dulling a few blades). An angle grinder with a metal cutting disk will work but magnetism is destroyed above the Curie temperature (about 500° C) so you should cool the magnet often as you cut through it (beware of sparks and bits flying off - wear protective clothing, ear and eye protection!).