Remove the existing finish in and above the crack with 220-grit sandpaper, paying attention to avoid removing the finish around the crack or split. Wipe away the sanding dust with a tack cloth. Remove any sanding dust inside the crack with a toothpick.
Mix the water-based wood putty according to the package directions. Choose a tinted wood putty that closely resembles the mahogany piece’s coloring.
Work the water-based wood putty into the split with a plastic putty knife. Load the product on the end of the putty knife and scrape it across the damaged area, working the putty inside the crack as you go.
Wipe away the excess wood putty with a damp kitchen sponge immediately. Allow the wood putty to set according to the package directions.
Sand down the excess putty from the crack or split with 220-grit sandpaper until it is flush with the surrounding wood. Wipe away the sanding dust with a tack cloth.
Apply a thin coat of varnish, shellac or the wood’s existing finish with a natural-bristled paintbrush. Allow the first layer of finish to dry for at least eight hours before applying a second coat.