Mac mini (Mid 2011) running extremely slow

Ways to help make a slow Mac faster

1. 17 Reasons Why Your Mac Runs Slower Than it Should
2. Slow Mac Performance? This Article Solves It!
3. Fix slow start-ups in OS X | MacFixIt - CNET Reviews
4. How to fix slow shutdown and startup times. | MacTip.net
5. 6 Easy Tips to Speed Up OS X Yosemite on Your Mac
6. Visit The XLab FAQs and read the FAQ on speeding up your computer.

Avoid using any third-party cleanup software. Usually, this software does more bad than good. You don't need it. All computers become slower over time even under normal use. Experienced users erase the hard drive and do a clean install from scratch from time to time; or whenever installing a major OS upgrade. Doing so means you must maintain regular and multiple backups.

Add more RAM or cut back on the number of concurrently running applications and utilities. Remove unnecessary anti-malware software and any software that promises to clean your Mac. Check for runaway processes: Runaway applications can shorten battery runtime, affect performance, and increase heat and fan activity. Also, visit The XLab FAQs and read the FAQ on dealing with The Spinning Beach Ball of Death.

The Ultimate Fix

Backup everything, erase the drive, reinstall OS X, and restore your data from the backup. Reinstall third-party software from original media/scratch.

Use Activity Monitor to Kill Runaway Processes

Use Activity Monitor on your Mac

Runaway applications can shorten battery runtime, affect performance, and increase heat and fan activity.

Hello,

I see you're having troubles with your Mac mini, and also see you've got a great Intel processor as well as a great amount of RAM; which does not explain such slowness as you describe it.

Have you tried opening the monitoring activity app on your mac to see if eventually a process is taking up large amount of RAM or monopolizing disk's full access?

You can also try reinstalling from scratch, the whole system, and updating to macOS Sierra when it'll be available, as it may possibly fix those problems.

Download and run Etrecheck. Copy and paste the results into your reply. Etrecheck is a diagnostic tool that was developed by one of the most respected users here (and recommended by Apple Support personnel) in the ASC to provide a snapshot of the system and help identify the more obvious culprits that can adversely affect a Mac's performance.