Is it possible to use external storage to store Attachments in Salesforce?

Yes this is possible but in that case you need to have external server where you can have your files/attachments and give a link of file in salesforce to download that file. When user clicks on that link, you need to perform the authentication and download the file by using external system APIs. Many servers are available to store your files like rackspace, amazon e.t.c. Let me know if you need more info on this.