I normally hand grind special lathe tools. To really get accurate a surface grinder works well. Never tried to do it on a CNC mill, but I guess it could be done if you wanted to hang a grinding wheel on the spindle, but this would not be my first choice. I like to avoid throwing sparks around machine tools. Step over would have to be very small.
You can grind in both directions.
Grooving inserts are inexpensive also.