Your automated tests are currently set up to answer the question "What isn't working as expected?"
Now you want them to answer the question "What isn't working that I don't already know about?"
Your solution is to change the automated tests so that they account for the "known" bugs in one of two ways:
- You could comment out the tests which find every known bug, so that they don't execute
- You could change the tests which find known bugs to temporarily look for the failure condition, rather than the expected condition
Be careful with either of these solutions! They require you to constantly update your tests every time you write a bug report. And you must remember to re-set your tests whenever you want to again ask the question "What isn't working as expected?"
One other trick (which I have used in the past) would be to leave the tests as they are, but save the output log from your automated tests, and compare it to the prior run. That diff would tell you "What is different in today's run as compared to yesterday's run?" If the log is constructed correctly (for example, log only failures, and never log the current date/time or other dynamic data), this could help give you the answer you need.
The difference between yesterday's log and today's log will indicate any new bugs found in today's run, as well as any old bugs that were fixed in today's run.