External GPU allow a late 2014 mac mini run 4k at 60Hz? Would an external GPU allow a late 2014 mac mini run a 4k display at 60Hz? 

Or would the CPU in the mac mini prevent this.
In theory, yes - an eGPU could allow you to run a 4k display at 60 Hz. It depends on the specific eGPU (i.e. which graphics card is actually plugged into the breakout box).

The CPU in your Mac Mini is not going to be the limiting factor for running 4k at 60 Hz in itself. However, it might be that some games/applications that you would like to run do not run with optimal performance on that Mac Mini. You'll have to test and judge yourself.

The reason I say "in theory" is because Apple has made it so that eGPU support on the latest macOS requires Thunderbolt 3. Your Late 2014 Mac Mini only has Thunderbolt 2, so it is not officially supported.

Some community scripts exists to allow eGPU on Thunderbolt 2, but obviously the performance is not going to be the same.