Its possible to run grunt tasks within webstorm through external tools. However, is it possible to avail debugging with external tools? By running tasks like 'grunt server' or 'grunt test' within webstorm, it would make debugging a lot easier if it's possible with external tools like grunt.
You have to run grunt-cli as a Node application:
/Users/someuser/nvm/v0.10.5/bin/nodeGruntfile.js directory, ie /Projects/someprojectgrunt-cli symlink created on your node bin directory, WebStorm will use the symlink target), ie: /Users/someuser/nvm/v0.10.5/lib/node_modules/grunt-cli/bin/grunt
(C:\Users\someuser\AppData\Roaming\npm\node_modules\grunt-cli\bin\grunt on Windows 7)testClick on Run or Debug and you are done :)
I just happened to try this in WebStorm 10 today. I'm not sure if it's a new feature but WebStorm have integrated the steps described by @diego so you don't have to perform them manually:
You can set breakpoints etc. in Gruntfile.js just like you would any other file.