Is the engine stuck in the down position or the up position? In either event, perhaps it is something as simple as the reverse or tilt lock keeping the engine locked in whatever position it is locked into, perhaps the linkage is busted/messed up. Can the engine be moved at all, even the slightest little bit? If so, chances are good that the linkage is your problem.
In any event, I sure would NOT cut those shocks off unless you are positive one or both is frozen. And, like Frank says, the shocks wouldn’t be my first guess.
You are in for a big job if the problem is not linkage related. Try loosening the big tilt tube nut, perhaps that might help. You mention the steering cable is frozen into the tilt tube, that in itself would not keep the motor from tilting up and down though. Is the steering cable cut off? If not, there is a chance that the cable is good, just stuck into the tilt tube. Loosen/removed the steering cable locknut and see if the cable can be moved with the helm now.
If the shock(s) are indeed frozen/locked up, you will need to remove the motor from the boat to get at the pins and shaft holding them in. Sometimes beating on these pins/shafts with an air hammer helps free them up for removal.
Feel free to post pictures if that will help.
PS- Before you get tooooo deep into this labor intensive project, you might want to do a compression test and drain the gear lube to make sure the rest of the engine warrants working on the tilting mechanism.