SATA hard drive selection by mechanical switch
XY problem.
Easy way: get a 2-bay drive enclosure, and pull out the drive you don't want to mount. Some of these enclosures even support live hot-plug, which sounds a lot like what you're trying to accomplish.
Light effort: choose drives that require only 12V, and use a SPDT switch to select which one gets 12V power (hack it into a 2-drive &quot;Y&quot; power cable.) This won't necessarily hurt the drive, but yanking power suddenly could leave the drive with a corrupted file system if it isn't cleanly unmounted first. Yes, this uses 2 SATA ports. There's no problem with having SATA connected to a powered-down drive. More here: https://www.extremetech.com/extreme/82086-build-your-own-sata-hard-drive-switch/2
Don't bother: mechanical switch on SATA signals. Bad idea; it's a signal integrity nightmare.