Which kind of tree produces the hardest wood?
The hardness of wood can be measured by the Janka hardness test developed by Gabriel Janka.
The highest value measured currently is the Australian Allocasuarina luehmannii (also called buloke or bull-oak).
Oh wow, that is super interesting! Can you still use a normal axe to chop this wood? Or does it even break a chainsaw?
Wood with an exceptionally high Janka hardness, like the Allocasuarina luehmannii, can be very difficult to cut and chop with standard tools. Some key points:

It would require a very sharp axe and a lot of force/effort to chop through this wood with an axe. A dull axe would likely just bounce off or get stuck.
It can dull chainsaw blades quickly and may require a more powerful chainsaw.
It can be hard on power tools in general and shorten the lifespan of cutting discs, blades, etc.
It may require pre-drilling and screwing/bolting instead of nailing due to how hard it is.

So while you can cut it with the right tools and blades, it does present more challenges than typical softer woods. The extreme hardness is what makes it durable for uses like flooring or construction, but that same hardness makes it much more difficult to work with manually or with standard tools.