What year Mac Mini do you have?
If you used Mac Post Factor I'm stipulating you have an unsupported Mac. 10.10 supports Early 2009 or later so I imagine you have a Mac Mini even earlier than that?
The graphics card is likely terrible in your machine, which is why the graphics are choppy and partly why the system is unsupported in the first place. You may also be hitting the I/O limit of the drive and if it's corrupted this would compound performance issues. Furthermore if you have integrated graphics which are shared with system RAM, anything less than 4GB RAM would also contribute to sluggish animations.
In conclusion: if you could provide specific details about your machine it would be helpful. However from your description it's more than likely you're hitting hardware bottlenecks which is causing the poor performance.
[doublepost=1495580182][/doublepost]Ah, saw your other post. You have a 2007 Mac Mini with Intel GMA 950. The graphics suck on it and they were terrible even for the time. That iGPU barely runs Lion animations smoothly, let alone Yosemite.
The hardware can't handle the OS. It's why your Mac was unsupported in the first place.