On my style strut cutting the shaft would not help. There is a shoulder that the mount sits on below the nut. If you cut the shaft you'll get the strut and mount off...but you'd still be stuck trying to get the nut off to reuse the mount....or in my case
camber plates. Depending on the room you could cut the nut off.
Like stated previously....make sure the weight of the car is on the control arm. That spring can fly out and kill you or your cat ( if ya have one )...or the dog...or maybe even a neighbor. Doing struts are one of the most dangerous jobs you can do.
At work the vise grips always save the day. Vise grips and an impact gun. A 1/2 breaker bar and a piece of pipe on the end will work too.