Lift the bottom of the tiles above the broken one about 2 inches using a pry bar to gain full access to the damage tile. Wedge a small piece of scrap lumber under the tiles to hold them up.
Remove the loose cement tile by pulling it free from its cracked mortar. If necessary, tap the tile lightly with a hammer and chisel to break it into smaller pieces to work it free from its location.Another method is to drill a row of small holes in the tile with a carbide-tipped drill bit. Take care not to drill into the roof's sheathing.
Pull out all the remaining mortar. Check the roof's sheathing and paper to ensure there is no damage. Make repairs to them, if necessary. Remove any nails that may protrude from the roof.
Dry-fit the cement roof tile. It should sit at the same level as the others and be snug in the opening. Cut the tile, if necessary, using a wet saw with a masonry blade.
Apply grout to the back of the replacement tile, using a putty knife. Slide it into position. Allow the grout to dry according to the manufacturer's recommendations. Temperature and humidity may affect drying times. Remove the wedges from the tiles above.
Work additional grout around the edges of the tiles with a putty knife. Wipe off the excess.