やっと希望の動きしてくれた。いろいろチューンナップしよう。

Gruntfile.js

var path = require('path');
var lrSnippet = require('grunt-contrib-livereload/lib/utils').livereloadSnippet;

var folderMount = function folderMount(connect, point) {
    return connect.static(path.resolve(point));
};

module.exports = function(grunt) {
    var pkg = grunt.file.readJSON('package.json');
    grunt.initConfig({
        compass: {
            dev: {
                options: {
                    config: './config.rb'
                }
            }
        },
        cssmin: {
            compress: {
                files: {
                    './css/style.min.css': ['css/style.css']
                }
            }
        },

        connect: {
            livereload: {
                options: {
                    middleware: function(connect, options) {
                        return [lrSnippet, folderMount(connect, '.')];
                    }
                }
            }
        },

        // Configuration to be run (and then tested)
        regarde: {
            reload: {
                files: '*.html',
                tasks: ['livereload']
            },
            sass : {
                files : ['sass/*.scss'],
                tasks : ['compass','cssmin']
            }
        }
    });

var taskName;
for(taskName in pkg.devDependencies) {
    if(taskName.substring(0, 6) == 'grunt-') {
        grunt.loadNpmTasks(taskName);
    }
}
grunt.registerTask('default', ['livereload-start', 'connect', 'regarde']);
};