First be sure that the file you want to read is JSON syntax.

Then it’s a shot “with the bullet though the back into the eye”, as we say in germany:

   // Getting gile myFile.json file
   var file = Mojo.appPath + 'myFile.json',
   fileFromAJAX = new Ajax.Request(file, {
     method: 'get',
     parameters: '',
     evalJSON: 'force',
     onSuccess: this.fileReadCallback.bind(this),
     onFailure: this.fileReadErrorCallback.bind(this)
   });

MainAssistant.prototype.fileReadCallback = function(transport) {
   var resp = transport.responseJSON;
   this.myVar = resp.myVar;  //Here you can access your variables in your json file.
};

That’s it.
I hope they will change this in future versions of WebOS.