Mid '11 Mac Mini boot loops at Apple logo, but can boot to Safe Mode
Reinstalling from Recovery mode should work. Here is how to enter recovery mode. On a normal working computer, it usually takes a few tries to get into recovery mode as the timing is very important. Maybe try a few times to get into recovery mode. Make sure you go into the regular Recovery Mode and NOT Internet Recovery Mode.

Another thing you could try is to see if it is a hardware problem or a software problem. You could check this by creating a bootable usb drive with another OS(it doesn't really matter which OS) and attempting to boot into that OS on your Mac Mini. If booting into another OS works, you'll know it's a software problem.

If you have access to another Mac use this guide(by osxdaily) to safely install macOS onto your Mac using a bootable USB drive or use this guide(by apple).

If you need a .dmg file for macOS/OS X(to create a bootable USB on non macOS/OS X systems) try this link.