Well, it would be easier to tell you how to go about it, if you'd post a photo.
If by 'skirting board' you mean base trim, or cove, then the basic premise will be to pry it loose with a small prybar.
Often, there is paint, or caulk along the top edge of the trim, against the wall, so it is handy to use a utility knife (razor) to cut the paint seal first. Then, slip a stiff putty knife down behind the trim, and pry forward with it. Get the trim worked out just a bit, and you can use a prybar for quicker removal. It's a good idea to put a thin material (cardboard, or a small piece of wood for example) behind the prybar, so you don't scuff up the wall itself.
http://www.creativehomeowner.com/images/chele169fig3.jpg
http://www.kwickkleen.com/catalog/images/2904-5600.jpg?osCsid=02d4350c9439d5910b060a071a2b5365
http://greatnecksaw.com/images/product_images/preview/125ST.jpg
Then you can decide how you want it cut, and reattach it to the wall.
Have Fun
Additional:
Well, it IS possible in some cases to saw the wood in place -- again, it would have helped if you had provided a photo.
There are a couple of tools you can use to make a relatively clean cut - I say relatively, because it will not be as good as removing the trim, and using a miter saw.
You can try using a hand saw, something with a short length would be best, and you must be careful with it, or you can damage the wall itself. Something like one of these -
http://www.rockler.com/product.cfm?page=19722&filter=hand%20saw
or a 'hardback' saw (often used with miter boxes in trim work - 'old school style')
If you want to spend a little money on a power tool, then you might look at something like these -
http://www.mcfeelys.com/product/MULTI-MASTER/Fein-MultiMaster
The way this tool works is it moves the tool head side to side, as opposed to rotating, or forward and back, like other tools. This makes it very handy for work in tight locations.
The other option, and one that is slightly less expensive, would be the Dremel rotary tool, with a cutter. You can find Dremels at many locations these days, including stores like WalMart.
Feel free to email me, if you have any further questions
Good Luck