Cut a magnet into smaller pieces

It is impossible to cut a speaker magnet with a hacksaw because the magnet material is harder than the hacksaw teeth.

You can break a magnet into smaller pieces by scribing the break lines onto the magnet surface with a single point diamond scribe and then flipping the magnet over and striking the backside of the magnet surface with a hammer and chisel, where the chisel edge is aligned with the direction of the scribe line on the opposite side.

But the best way to accurately separate a magnet into smaller pieces is with a diamond-wheel grinder.

Note that the most common magnet material used in big and cheap loudspeakers is barium ferrite. This is what your magnet is made of, which is not the strongest magnetic material available. Small rare earth magnets are on a per pound basis far stronger and can be bought cheaply in a variety of shapes.