Graphite has specific properties that make machining a challenge. It’s strong, but also brittle, and is susceptible to chipping if not handled properly. Cutting Graphite (or carbon) is different from cutting Metals. Metal exerts plastic deformation when a tool edge cuts it producing a curl or chips. When graphite is machined small powder-like particles separate from the work piece as a result of brittle fracture caused by the stress produced by the cutting tool edge. Graphite machining can be challenging. Especially if you are not prepared to work with its unique and messy properties.
Sometimes people misunderstand the phenomenon that carbon can be dissolved in steel, so that it is not possible to machine steel with diamond or diamond coated cutting tools. Carbon atoms from the cutting material dissolve into the material being machined. With dissolved we just mean that the carbon from our cutting material fills up the spaces between the atoms in another material. So we can say that the atomic structure of a certain material has room between their atoms.
Possibilities
Steel is steel and High Speed Steel (HSS) is also steel, but then hardened. The structure of the material is different making it harder.

In steel is this no problem at all, lots of space between the atoms.

In the diamond structure there is no room for extra carbon atoms, the matrix is completely stacked with carbon atoms that are very strongly connected with each other. And diamond is a lot harder than graphite because it has a tetrahedral structure. In all directions the carbon atoms are very strongly connected.

In a pure grid light can penetrate through the grid, hence a pure diamond is transparent. Flaws in the grid structure scatter the photons of light and change the wave length making them bend what creates the lovely rainbow effect.

Graphite is also a structure of carbon atoms, but this structure is flat, creating a kind of layers (see picture below). If you press the structure from the right direction, the layers will easily separate. These layers are randomly distributed in graphite, so from whatever direction you push (machine) layers can always be removed from each other.

Graphite, however, is very hard when you press it from the "wrong" side, which is why it is very abrasive, when machining graphite we don’t make chips (swarf), so there is relatively long contact with the graphite and the cutting edge (environment) which leads to very abrasive wear on the cutting edge.
So, instead of making chips when machining graphite we create very fine dust. This means that safety and health precautions need to be made when machining these materials.

Links
https://www.secotools.com/#article/67339
http://www.semcocarbon.com/semco-carbon-blog/five-keys-to-success-when-machining-graphite
