For a simple test case, suppose we have a 10 km cable, 1 cm2 in area, 1 g/cm3 in density, and 100 GPa/(g/cm3) in tensile strength.
Specific strength in KYuris should be 100,000. Breaking length in km is derived from that by dividing by 9.8, so it is approximately 10,000 km (1000 times the specified length).
Linear density for such a cable (i.e. a square centimeter across and the density of water) is 100 g/m which is 100 kg/km. Thus the cable as a whole (at 10 km) weighs 1 ton.
Assume a 100 ton spacecraft deploys the cable with a harpoon to a target moving 1 km/sec relative to itself. The harpoon has to accelerate pretty rapidly to match with the target, as does the cable itself (which we've imagined to be on a spool, which spins up to 1km/sec right away). Once this step is complete, the craft loses momentum over time by providing tension on the cable and thus accelerating the target comet/asteroid, which consumes enough momentum to make the acceleration of the cable in the craft's direction very slight.
Assume the craft needs to lose 1km/sec over the 10km length of the cable. 20 seconds and 50 m/sec2 of acceleration (approximately 5 gees) would suffice for this. The 100 ton craft is 100,000 newtons of force per m/sec2. That adds up to 5 million newtons. The cable should be able to handle 100 million newtons.
If we want to go to 10 km/sec, 100 times the cable length is needed to do it at the same (5-gee) acceleration rate. The length is 1,000 km in that case and weighs 100 tons, which is the same as the craft now. The craft could still accelerate along it at 5 gees and only produces 5 million newtons of tension on the cable.
Since that's 50% payload fraction, this basically does match your graph.
On the other hand, it's not completely set in stone at that efficiency. Say we change the acceleration rate to 50 gees (for a tough robotic craft). That cuts the tether length needed to 100 km (and mass to 10 tons) at a cost of increasing the force per unit mass by ten times. It's now 50 million newtons, i.e. 50% of the cable's capacity.
Regardless of that, about the only obvious way to make this significantly more profitable than rockets (especially ion) for these kinds of high velocity shifts, without increasing the acceleration to something a human could never handle, would be to use the same tether multiple times. You could use the same cable to jump between several different asteroids moving at rates in the 1km/sec range until you reach the delta-vee of the comet, with essentially no expenditure of reaction mass or significant energy. That gives it a pretty huge advantage over fuel, and even an ion drive (which needs energy and reaction mass).
Even better (for colonization, if not exploration), you could use these same tethers multiple times. Assume it can be grappled magnetically or with a set of spinning contact wheels of some sort, so there's no spooling of the tether involved. Once one tether is anchored by the first craft, you can land a whole fleet of ships on the same asteroid.