Bear in mind that we're talking about metallic tungsten here, not tungsten carbide (WC). It's a little slow and expensive but it can be machined in fairly conventional ways, using tungsten carbide tipped tooling.

Tungsten has an enormously high melting point, the normal way tungsten parts are produced, for typical industrial purposes such as radiation shielding, is sintering (powder + heat + pressure) to near-net-shape, finished with a machining pass.