Rendering is a very resource-intense task thus I'd highly recommend you to avoid doing anything else on your machine while rendering: it will either clutter the system or simply work out poorly.

Anyway, I suggest you to try rendering your final scenes or animations from the command line. I noticed that renders done that way tend to be kinda faster and the machine is more stable without the overhead of Blender's GUI.

 1. Make sure to set up your blend file so to make it use the GPU for rendering and make sure to specify all the output options (select a path, a filename, the file format, etc.). Save the blend and close the GUI.

 2. Copy the path to your blend file. Then, move into your Blender's executable path via Terminal (note that your path might differ, so I suggest you to also [see this answer][1]):
    `/Applications/Blender/blender.app/Contents/MacOS/blender`

 3. Run:
    `./blender -b "pathToYourBlendFile" -f 1`
(-b tells it to run in background, -f 1 tells it to render the first frame only).

Now the render should start with all of your preferences. Try to see if the system is more usable while rendering this way (mine usually is, but I suppose YMMV).

  [1]: https://blender.stackexchange.com/questions/2078/how-to-use-blender-command-lines-in-osx