Naz how can you cut off a section renew the olive and then rejoin a fixed pipe they dont stretch also where are you to turn the water off surely it needs to be investigated before you go and undue any fittings.
Is it hot is it cold is it part of the central heating that will need to be drained down, llamekuf be very care-full if you dont want to be flooded out.
When you find how to isolate and there is no more water issuing from the nut of the fitting as scotman pointed out,very carefully undo the nut that has the leak making sure you have plenty of old towels/buckets around,in case water comes out and you have to do it back up quickly,if you can clean between the olive and the fitting body put 3or 4 turns of ptfe tape round at this point ,tighten the nut to trap the tape between the fitting and olive.
You could be very brave however and just try to tighten the nut up by holding with two adjustable wrenches,one on the nut one on the body, but i would still isolate the water in case it goes wrong. HTH Tez