Back out the screws holding the threshold in place using a drill and Phillips driving bit. If the threshold is nailed in place, insert a reciprocating saw blade between the threshold and subfloor and cut through the nails.
Pull out the threshold from underneath the exterior door's side jambs. In most cases, you will need to pry away the toe kick — the vertical exterior board underneath the threshold — with a pry bar before you can remove the threshold.
Draw a square around the damaged subfloor to mark the portion to remove. Look inside the square for any nails or screws. These indicate where the floor joists run. Extend the square's sides to the nearest floor joists on both sides to form a slightly larger square.
Set a circular saw to the same depth as your subfloor, usually 3/4 inch. Cut the square out of the subfloor. Make sure to cut around the nails or screws so the remaining subfloor will remain attached to the floor joists.
Measure the opening's dimensions with a tape measure and transfer the dimensions to a new piece of subfloor. Use these measurements to draw a square on the subfloor that will fit tightly inside the opening. Cut the square out with a circular saw.
Set the square into the opening. Secure it in place with 1 1/4-inch wood screws into the floor joists. Slide the exterior door threshold back into place and secure it to the new subfloor with nails or the screws you had backed out in Step 1. If you removed the toe kick, nail this back into place.