You could also use a client like Thunderbird, and set up a POP account (as opposed to IMAP), which will download all your email to a mailbox on your PC or Mac.
You can then go into SM webmail, for example, and delete whatever emails you'd like from there, and it will stay in Thunderbird, as POP mailboxes do not sync with the mail server (but they typically don't download the same email twice).
If you do go this route, please TEST this by deleting a couple of emails that you don't need from the mail server after downloading your email to Thunderbird, then re-sync Thunderbird and make sure that those emails are still there - you can then delete them from Thunderbird if you want. You may have to adjust your Thunderbird settings for deletion. I haven't worked with POP in awhile, so please double-check!
Your mileage may vary, so it's up to you to make sure this proposed solution works.