If your Mac's screen saver freezes and doesn't want to go away, don't worry. Many other users have come across this problem, but there are a few ways to fix it.
What Happens Exactly?
If your Mac's screensaver freezes, moving your mouse cursor around or hitting keys on the keyboard won't make it go away. The mouse cursor will appear on the screen and you can freely move it around, but the screensaver will still show.
The keyboard and mouse will still work, meaning that if you click your mouse or type on your keyboard while your screensaver is frozen, your Mac will still register it. Furthermore, your Mac may also never go to into sleep mode because of this and will remain on until you can fix the problem and get back to the desktop.
We're not exactly sure why it occurs, but it's a known reoccurring issue. I've personally seen it happen on my MacBook every few months or so, but there are a couple of fixes that you can try out.
Reset the NVRAM
The only quick, permanent solution that I've seen fix this problem is resetting the NVRAM (non-volatile random-access memory). It stores various OS X data like speaker volume, mouse and trackpad settings, and screen resolution.
Sometimes the NVRAM can become corrupted, which could cause an issue like this. Thankfully, you can easily reset it. Keep in mind, though, that this will reset things like speaker volume, mouse settings, date and time, and other small things like that.
To reset the NVRAM, start by completely shutting down your Mac. Next, press the power button to turn on your Mac, and immediately press Cmd+Opt+P+R on your keyboard. Keep holding those keys down until you here the startup chime for the second time. From there, let go and let your Mac boot up as normal.
Of course, you won't know if this has actually fixed the screensaver problem until it happens again. If it doesn't happen again, then it's likely that resetting the NVRAM helped.
Put It to Sleep Manually and Wake It Back Up
If you happened to be working on something important when the screensaver problem occurred (maybe you went to get a quick drink and came back to it), you don't necessarily want to force-shutdown your Mac in the middle of important work, so there's a temporary fix that will unfreeze your Mac's screensaver.
All you have to do is press down on the power button for about a second (a quick tap won't do it). This will manually put your Mac to sleep. From there, you can press on the power button again to wake it up and you should be back at your desktop.
Again, this is a temporary fix and it's likely that you'll come across this issue again at some point in the future if you don't take further steps, but it will at least prevent you from having to shut down your Mac and possibly lose any important work that you were in the middle of.