after the facia is removed in most cases, you have the rafter tails exposed, but behind the facia and on the underside is also the soffet and freze board.
Check out this anatomy of this area for more detailed look see of your project.
In direct answer to your question, this project is NOT that difficult at all, and I would NOT consider re using the facia once removed.
This is the steps I go through when removing the gutter and replacing either facia or soffett material: All the material I remove will NOT be re used since the removal process usually damages the material and renders it tacky.
1) remove the metal roof edge or drip edge. this protects the facia and channels the water off and away from the facia board. Then you have a furring strip usually under the drip egde that is normally a 1 x 2 material usually redwood. I remove that completely from the original end to the natural end.
2) The facia, I remove the entire length from end to end. You can however cut the section out that you want, but I like doing the entire lenght. This way you know that both ends are straddling a rafter tail and you can cut the 25 degree ends to match the other good ends. The facia will normally be 6 inch wide material and it can be the "plowed" material that is "plowed" to match the soffett thickness so you have a good tight fit. However, if you cannot find the "plowed" facia board, use regular wood and caulk the intersection of the facia and soffett or even use quarter round to finish out the intersection. If the material or facia was plowed then you will have a lip extending over the rafter tails of the soffett that was intended to fit inside the "plowed" trough of the facia. Most facia boards are enginerred redwood material.
3) now you have the drip edge off, the furring strip off and the facia off. At this point you can make a look see in the open area to determine if any rodents, wasp nests, or other varmits will be in that are when dropping the soffett area. This is the dirty part and wear goggles and mask as the debris could be very messy. Take out the bad soffett area. Go from one rafter tail to another to get a good fasten. If this is not feasible you will need to "sister" 2 by material for the soffett to attach to and butt up to the soffett that is OK. Again, I like to take out a complete section of soffett since I will know that will re fit back. But only take out as much old soffett as your facia goes.
4) Now make your measurements and attach your new soffett material. Mark the rafters locations on the freeze board or the siding next to the soffett so you will hit each rafter. Cut out any soffett vent holes that were there.
5) attach the new facia board. Mark your rafter tails again so that you don't go into air, but into the actual tails.
6) install the 1x2 all down the line. Then install the new drip edging.
7) prime the bare wood areas with two coats and do all the finish work, caulking and all.
8) Reinstall the new gutters allowing for the proper "fall". This time do not use the long gutter nails and ferrels, go with the screw in special gutter hangers.
This should be it. Its a one man job, and easy, but dirty.