Whenever I am trying to run my Elixir project on Intellij idea in mac OS(Elixir installed by brew) i get
/usr/local/Cellar/elixir/1.4.1/bin/elixir "" ""
No file named
My run configuration is:

project structure is:

@Istiakmorsalin did you setup the project using Import Project from External Model? Some users that open an Elixir project without using Import Project from External Model have reported similar issues in the past.
This looks like you don't have a mix path set. Here's what an "empty" Elixir Mix Run Configuration output looks like:
/usr/local/Cellar/elixir/1.3.2/bin/elixir /usr/local/bin/mix ""
So, the first "" in your output is the mix path, but you don't have that set. Looking through the code, I think the mix path can only be set on importing the project (I will count it as a bug that it's not accessible in any of the UIs, but we'll open that as a separate bug), so re-import the project using Import Project from External Model
I had the same problem, you can set mix path in "Other settings > Elixir External Tools".
Weird. I tried the suggestion by @oinopion but it did not work. I imported the project from existing source and it worked.
Weird part is, the setting mentioned by @oinopion was populated with the same value after importing as I had entered manually.
I should note too that I am on Windows and the plugin does NOT like spaces in paths. I created a symlink using mklink to a directory with no spaces and it works a treat.
The second "" is better explained in https://github.com/KronicDeth/intellij-elixir/issues/709, so closing this since no feedback from @Istiakmorsalin in > 3 months.
Most helpful comment
I had the same problem, you can set mix path in "Other settings > Elixir External Tools".