So you want to remove the coving from the ceiling/wall.
How old is the property ie how recently has the coving been put up?
They are normally stuck on using adhesive and also tacked on for extra mechanical strength whilst adhesive is setting.
The adhesive can be quite difficult to remove sets like shyt to a blanket!
So it will be very difficult to remove the coving without causing some damage to wall and ceiling, you can minimise this though.
If the walls and ceilings are plasterboard, I would firstly run a stanley type blade around all the adjoining edges of the coving to the walls and ceiling. Trying to cut in to the plaster/plasterboard, this should hopefully then help prevent tear damage to your wall and ceiling, when removing the coving.
If the walls are plastered then I would use a chisel and hammer and gently break in to the coving from the edges, prising it away as you go, you will also use this method after you have cut in to plasterboard with stanley. Then it would be a case of knocking of any left overs and scrapping and sanding as reqiured, plus any remedial work.
You are bound to cause some damage and there is nothing to say that the area under the coving was ever done to a good standard in the first place, if the person installing walls/ceiling knew it was to be coved, they may have left that area unfinished.