To remove all data on a drive you do a multiple run format. This means you write the data to a 1, then write it to a zero, and doing this multiple times ensures the data can not be reread. 1 pass is sufficient for 95% (anyone not in a data recovery lab), 3 pass is 99% and 7 passes would be 99.999% (7 pass is what is done by government.
Now for an SSD, doing this will shorten its lifespan. Most SSDs have a utility that will have it scramble all data and make it unreadable without reducing your ssd performance/lifespan.
ADDED:
Any partition program like Easus or Paragon Partition Master will have the ability to do a multiple pass format. If you just want a single pass format then you can use windows built in utility and just uncheck "quick format".
Now in regards to reading a damaged drive, top end labs can recover data off of fragments of hard drives. Doing the format is a completely sufficient means of destroying the data on the disk, but if say the drive is an old format that you have no ability to read then damaging the platters to the point the drive will no longer spin will make data recovery way to much cost/effort to be worth it to anyone wanting to do identity theft or hack online passwords.