I have cut regular bricks by cutting them in from both sides and they break cleanish. Sometimes from one side as well. Bit that is common red brick (boerke in my country).
There is a trick of breaking brick stones with the trowel. I can't but the guys building my walls did it with the boerkes, the ones with 3 holes or the massive ones. The bigger ones with holes in (speedstones, snelbouwers ??) Is done with grinder. To many holes inside for a clean break.
With firebrick i would cut it from both sides as deep as possible and than break. If it needs to be flat, a grinder (again normal stone, i used a dry diamont cutoff wheel on my grinder and used the same wheel for smoothing it out). With dry cutting, be aware of the dust.