I have used the old trick of placing the dead drive in a plastic baggy to seal it up then freeze it for a good 24-48 hours. Then remove it fast and hook it to your computer and you hopefully will be able to use it long enough to get everything off it. Freeze it s cold as you can make it.
But work fast and try to keep the drive from warming up. Wrap it with some insulating material to keep it cold for a while. This worked quite a few times in the past for me.
Another way that is very difficult but can work, (I have actually done it on 2 dropped drives that had the sata connections broken off), is to get a sacrificial drive, one you can afford to lose, and you open it up and remove the platters in it and take the platters from the dead one and install them then close it up. But it is very difficult and the sacrificial drive has to more or less then dead drives specs. You can google about that trick if you are desperate to see exactly all that is involved. Be ready for a learning curve.