I have been in a similar situation and successfully used TestDisk by CGSecurity (Open Source) to eventually recover almost all of the data from a crashed 500GB Crucial SSD. There are other free or commercial ssd recovery tools that will probably work as well (search for SSD recovery tool).
In my situation the SSD would also no longer be recognized by the BIOS. By putting the SSD in an external USB enclosure, TestDisk could find and access it, temporarily rebuild the partition table and copy most of the files to another PC.
I guess it depends on the particular damage to the SSD whether the same procedure will work for you. In my case the partition table was damaged and somehow the SSD became read-only. I have never been able to get it working properly again.