Intro: Cardboard Blade for Tablesaw
Fairly self-explanatory: a piece of snap-off-boxcutter-blade is glued into a slot cut in a stick of hardwood, then the assembly is wedged into the t-groove of the table saw. It's nice; using the fence is much faster and more accurate than guiding a boxcutter with a straightedge.
Use hot glue so that, when the blade gets dull, you can melt it and change the blade out.
While you could tilt the blade the other way, so that it pushes the cardboard down onto the table, it tends to pull the cardboard down into the hot glue, and so drastically increases the amount of friction. I suppose you could get fancy with the construction of the device - perhaps making it from UHMWPE, and using a screw to hold the blade in place - but how much cardboard do you really intend to cut?
If you have a table saw which was designed so that zero-clearence inserts are easy to make, you could make a cardboard-cutter insert - then the ruler for the fence might mean something.