If the drive in the 2011 Mini is still working, do this:
Download either CarbonCopyCloner or SuperDuper.
Both are FREE to download and use for 30 days, this will cost you nothing.
I like CCC.
Get CCC here:
www.bombich.com
Note: You didn't tell us WHICH VERSION OF THE OS is on the MacBook.
You want to download the correct version of CCC for the OS you're using.
When you get the Samsung SSD in your hands, do this:
1. Boot the Mini
2. Connect the SSD
3. Open disk utility
4. IMPORTANT -- check to see if the version of disk utility you have has a "view" menu.
IF it has the view menu, choose "show all devices".
(If there isn't a view menu, just skip this and go to next step)
5. You need to erase the SSD to get it ready for CCC
6. IF you're using High Sierra or earlier, erase to "Mac OS extended with journaling enabled, GUID partition format".
IF you're using Mojave or later, erase to "APFS, GUID partition format".
When the erase is done, quit disk utility and open CCC.
Accept all the CCC defaults for now.
You will see "three boxes" in the main CCC window.
You can turn off the "tips" if they're bothering you.
In the leftmost box (the "source" drive), click and select your INTERNAL drive (on the Mini).
In the center box (the "target" drive), click and select your SSD.
You can IGNORE the rightmost box -- scheduling not necessary.
Now click the "clone" button.
CCC may ask if you wish to clone the recovery partition as well.
YES, go ahead and do this if it asks.
The cloning should take a little while, be patient.
When done, quit CCC.
Open the "startup disk" preference pane.
Do you now see the SSD as a bootable drive choice?
If so, click the lock icon (if there is one).
Enter your password.
Select the icon for the SSD to make it the boot drive.
Close the startup disk pref pane.
Now, REBOOT the Mini.
Does it boot from the SSD?
You should know right away because the boot process may go more quickly.
Check the "About this Mac" choice (Apple Menu) to be sure.
If you print out and follow these instructions step by step, this should get you where you need to be...