This feature is supported in the Ultimate edition only.
In IntelliJ IDEA, you can launch Grails or Griffon applications using the regular procedures, with the dedicated Grails Application or Griffon Application run/debug configuration:
Note that IntelliJ IDEA enables you to debug *.gsp files: you can set breakpoints at the lines of the views, examine variables, and evaluate expressions.
Besides that, you can execute Groovy scripts that exist in Grails or Griffon applications. Observe results in the Run and Debug tool windows.