How did you think this was going to work?
If you only have a single SA Tivo the only ways to watch one thing and record another are to have two cable boxes, one connected to the RF bypass connector and the other to the Tivo inputs, or split the cable before it goes into the cable box. You would leave the cable box connected as it is and then take the other split cable and connect it to the bypass connector on the Tivo. This method will only allow you to watch the lower analog channels, not any digital channels that require a cable box. In the previous cases putting the Tivo in standby would let you watch the bypass signal, you would change the channel with the second cable box's remote (problematic since you will most likely have identical boxes) or with the television remote.
You could also split the cable and have one side go directly to another input on your TV. When you wanted to watch something else you would change the TV input. This case allows you to use your TV's PIP function.