.....but to what end.?
Substitute paint for dye. What happens to the paint when you use the cutting board.?

 

No. Analine dye is not food safe.

 

Fun fact: There are foods like hot dogs which contain analine dyes so I would stay it was food safe. I don't think the color would last very long. I think every time the cutting board was washed you would see the color fade.

 

Aniline Dye is food safe and toy safe, especially when water is used as the base.....when thoroughly dry.

Dried shellac is food safe.....when thoroughly dry.

Polyurethane is food safe.....when thoroughly dry.

Even Zinsser Bulls Eye Sealcoat is food safe.....when thoroughly dry.

There are also formaldehyde free topcoats which further employ finishes that are food safe, for example, cutting boards and baby safe, for baby cribs and beds as another example.