Can uglify-js remove the console.log statements?

There’s also another option called drop_console which has been added recently (late 2013)

drop_console -- default false. Pass true to discard calls to console.* functions

This is added to the grunt init config like this:

grunt.initConfig({
  uglify: {
    options: {
      compress: {
        drop_console: true // <-
      }
    },
    my_target: {
      files: {
        'dest/output.min.js': ['src/input.js']
      }
    }
  }
});

As taken from the grunt-contrib-uglify github documents