Sharp cutting tools are absolutely crucial for cutting metal. But a 60 grit grinding wheel is not really a sharpening tool- it's for shaping only. Sharpening has to be done in addition to shaping, and any improvement in your cutting edge using a coarse grinding wheel is really by luck.
These are what I use for sharpening my cut off blade and lathe bits-
Diamond lapping tools. They do a very nice job- the only trick is holding a consistent angle while sharpening. Someday I'm going to make a jig for holding and sharpening bits....