Okay you're starting to get. I think the most important thing to remember about the BJT is that it really is just two pn junctions and that cut-off, saturation, and active are just three combinations of those pn junctions being on/off.
So in cut-off both junctions are off. That means very little (or, in approximation, zero) current is being conducted through the junctions. This means I_B and I_C are both approximately zero. How do we verify this is true? We use the assumption that I_B and I_C are zero and solve for V_BE and V_BC and see if they are large enough to turn on their respective junctions.
If I_B = 0, then we can see that V_BE < 0 since 470k < 1M, which satisfies our constraint. If I_C = 0, then V_BC < 0 as well since there will be no drop across the 10k resistor. Therefore the conditions for cut-off are satisfied.