You can drill a hole in a magnet, although magnets are extremely brittle, hard and heat sensitive.
If you drill a hole through a magnet it may lose magnetism but mainly due to the heat generated by the drill bit when drilling the magnet.
And neodymium magnets also often have a surface hardness of RC46 which can ruin standard drill bits.
And the process of drilling a hole in a magnet can also cause the magnet to shatter, catch fire and lose it's magnetism.
Drilling a hole in a magnet also often results in chipping and cracking of the magnet.
The reason it's so hard to drill through a magnet is because of brittleness and fragility.
Magnets, especially the neodymium and ferrite magnets are brittle and can also break very easily and even shatter when you drill through them or saw them.
High heat during drilling of the magnet can also demagnetize or weaken the magnet.
So while you can drill a hole in a magnet or saw through a magnet it's not recommended.
A magnet's magnetic field can also be demagnetized by reversing its polarity, this can be done by placing the magnet in a magnetic field that is opposite to its own.
The opposite-field cancels out the magnetic field of the magnet, which reduces its strength.
There are a few ways to remove a magnetic field from a permanent magnet.
One of these methods requires increasing the temperature of the magnet.
Another way to make a magnet lose its magnetic field is by hitting it.