You can cut the pipe and use a compression coupler in almost any place - all you need is enough pipe to connect the two (or more) compression fittings.
I would recommend however that you try to remove the olive - look at ChrisR's post - point 3 or use a junior hacksaw on the olive. When you've removed the olive you can make a decision on if you need to cut the pipe back...
From experience, if it's been tightened enough to crack the nut - chances are the olive has badly deformed the copper pipe and it will be difficult to get a good seal with a new olive... but you'll not know until you remove the old one.
If you do need to cut the pipe - try to use a pipe-cutter rather than a hacksaw - much nicer cut with a lot less burring = better seal.
If a reason for not using a flexy is that it's visible on a downward-pointing tap tail on a basin, fit a right-angled compression tap connector to the tap and remove the nut and olive. As long as you use one of the most common makes, the flexy tap connector's "tap" end will screw straight on to the compression end of the fitting you just put on the bottom of the tap.
If you type in olive removing tool and olive puller in google, there's a loads merchants selling them, price do differ though !
Edit:I see your question already answered, I was still on page 1 !
The only problem with the olive removing tool is you would need 15mm & 22mm. The olive puller can do both 15mm & 22mm ! Has anyone use a olive puller ? or is it best to buy the 2 olive removing tool ?
If you need to find a tradesperson to get your job done, please try our local search below,
or if you are doing it yourself you can find suppliers local to you.
Select the supplier or trade you require, enter your location to begin your search.
Please select a service and enter a location to continue...
Are you a trade or supplier? You can create your listing free at DIYnot Local