Locate the nearest screws or nails that fasten the plank to the joists beyond the damaged section. Draw a line, just to the damaged side of the fixings, from one side of the plank to the other. Don safety goggles. Cut along each line with a sharp chisel, to a depth of about 1/8 inch.
Check for pipes and wires running under the damaged plank. Use a metal detector or pipe and cable detector and mark any positive responses on the damaged plank so you are aware of the potential risk areas.
Insert a floorboard saw between the damaged plank and the adjacent plank. Cut through the tongue at a point indicated to be free of pipes. Cut along the full length of the space between the boards, stopping at each joist. If the damaged section spans several joists stop at each one, and restart the cutting process on the other side.
Drill through the center of the board at each end, close to, but not into the joist. Insert a floorboard saw or a jigsaw and cut across the width of the board at both ends.
Don strong gloves. Insert a bolster chisel into one of the cuts, or into the slot where the tongue has been removed, and then gently lever the plank upward. Remove any remaining nails with a claw hammer -- they become obvious as the plank is lifted -- and continue to lift the plank gently. Slide the plank out of the floor, moving it away from the tongue of the next plank.
Remove the wood remaining over the joists at each end by trimming it back with a sharp chisel. Cut vertically to leave a clean and straight edge to the healthy planking.