Rip out the joints (inside the stove) 1-2 cm deep.
Water thoroughly in several rounds.
Grout with regular mortar.
I usually throw in fairly loose mortar into the joints, as it adheres well to the brick.
Wash across the joints with a damp cloth before it has fully hardened.
Let it stand, preferably for a month before lighting a fire, if you're going to light a fire. If so, only small fires to begin with.
If any stone is bad, just drill it out and grout in a new one with the same mortar as above.
- Do something similar in my large soapstone stove in late summer. However, this is not about grouting, but applying approximately a 1 cm thick heat-protective layer on the walls of the firebox. Use fireproof clay with ceramic crush. This is done in the same way with thorough watering in late summer. Hardened and dry by late autumn. Start with very careful firing during the first week, initially every other day.
Why? Although the firebox is built of soapstone, there is some burn-off of the stone surfaces after more than 15 years of daily firing during the cold season. Expect at least another 30 years of firing before possibly needing to replace an occasional stone in the firebox.