Some spam gets killed automatically. Some gets flagged either by filters or by users (there is a flag button on stories after you get over a certain karma), and killed manually by editors. It's very rare now for a spam not to at least get flagged.
I think there are algorithms in place that auto-flag spammy submissions to bring them to the attention of moderators more quickly, but as far as I know, actual deletions are manual.
BTW, when you say "aggressive about killing spams", you mean killing manually, right?