When deleting a comment (http://www.livejournal.com/support/faqbrowse.bml?faqid=15) you will be given an option to also mark the comment as spam. To do so you first need to select the "delete comment" button. This will then bring you to an intermediate screen where you confirm your action. You can mark the message as spam by selecting the appropriate check box on this screen before confirming via the "delete comment" button.
It is not possible to mark a message as spam when deleting comments using the "mass action" option.
When you mark a message as spam, this information is sent to LiveJournal administrators who are then able to take the appropriate action, for instance by suspending the spammer's account. Please note that all such information is carefully reviewed by a human being before any action is taken, so it is not possible for erroneous or accidental marking of messages as spam to result in incorrect action being taken. Even so, please only use this option if you believe the message in question to be spam (unsolicited bulk messages).
If you believe you are being harassed in comments, you should not mark them as spam. Instead, you can find guidelines on what steps you can take at http://www.livejournal.com/support/faqbrowse.bml?faqid=108.