The TiVo outputs only one video stream (the same content appears on component and HDMI outputs), so if you watch the local TV and via Slingbox simultaneously, both viewers will see the same live or recorded content.
Depending on your equipment and where it's located, you may be able to have limited simultaneous viewing of different programs. For example, split the incoming cable and feed the antenna input of your TV. You'll be able to watch a non-encrypted live program on the TV, while watching the TiVo via the Slingbox.
What other cable boxes do you have? What outputs do they have? How are they presently used?