You could work pure diamond into something shaped like a knife, but it wouldn't make a very good knife. Diamonds are hard, but they're brittle. The blade would break long before its edge went dull, but this is arguably worse: you can resharpen a dull blade, but a broken blade (especially one not made of a material that can be melted and reforged) becomes essentially useless.
If this is for a story, then one possible subject for research might be the macahuitl: a swordlike weapon used by the Aztecs. The main body of this weapon was a simple shaft of wood with grooves running along its edge, but small blades of sharpened obsidian would be fitted into the grooves. A blade could chip or break, but the weapon itself would remain intact through most blows, while the scalpel-sharp obsidian could cut even better than metal (seriously: obsidian is dangerous stuff). Modern "diamond knives" work according to a similar principle: only the edge is made of diamond, while the main body is made of metal, or something else that's not so prone to breakage.
For the purposes of a story, I could imagine the diamond-knife concept being scaled up into a sort of "neo-macahuitl" that used diamond blades. The main body of the weapon could be made of metal, hard rubber, or any other material of sufficient strength, and then small diamond blades (all diamond, or diamond-edged metal) could be fitted into it. It might even be possible to make the blades replaceable.