How is wafer dicing economical (for small ICs)?
In general: Yes. You're losing area through the dicing street as the way the saw runs through is called.
However, your assumption of the thickness is wrong. The saw is more like a thin foil. Usually around 20 micrometers thick (factor 25 thinner than you assumed) and I've seen very specialized ones that were even thinner around &lt; 8 micrometers. As a comparision: Typical bond wire pads (where the wires are connected to the Chip) are around 30-50 micrometers big. So your saw is thinner than the outer pad ring of the chip.
If you have a dicing saw in your hand it's kind of wobbely and does not very much look like a &quot;saw&quot;. It is only able to cut the wafer because it is spinning at very very high speeds, which  stabilizes the blade. The saws also have a very limited lifetime becuase of their small thickness. Usually they can only cut a few thousand meters before they need replacement.