Get a cable splitter. Run one cable to the Slingbox, Run the other to the Cable box.
Connect cablebox output to TV, not to Slingbox.
Connect nothing to output of Slingbox.
Go to Setup on Slingbox.com to configure the Coax input.
You will only get basic cable, no premium channels.
If you want the ability to sometime watch what the cable box puts out and other times what the basic cable coax supplies read more here.
No, the whole idea behind the Slingbox is to transmit over the the Internet to anywhere in Internet Land the programs that ARE being broadcast through the cable coming out of your wall, or your cable box, or your DVR -- depending on where you put the Slingbox into the system. But, if you have your TV connected as a direct passthrough to the signal input that is going into the Slingbox, then the TV will mimic whatever you are commanding the Slingbox to do. So, if you command the Slingbox to change channels, and the TV is connected ONLY to the Slingbox, then the TV will change channels too.
To sling one chanel while watching another channel on the TV, you need to have your TV (also) connected to a signal input that is NOT going through the Slingbox. Hence, putting a signal splitter upstream of the Slingbox -- typically right after the cable signal comes out of your wall outlet -- so that the TV can get a signal input that is NOT coming from the Slingbox. You then use the remote of your TV to switch its input signal between "Video 1", "Video 2", etc. -- using the method appropriate to your TV model for connecting multiple input signals to it.