Electronic – How to modify this circuit for variable clipping without affecting gain

First, the DUT is in the positive feedback because this way you have an inverting and a non-inverting gain in the loop, so that multiplying them you obtain an overall negative loop gain.

Second, the gain is 1000 because Vin of DUT is Vos*50/(50K+50), so if you consider that V+ of the DUT should be 0, there is only the offset applied, so the feedback forces the output to be 1k times the offset voltage.

I think that you can look at the output this way: suppose that the situation is the one described, and you have a 500uV DUT offset and so 500mV output voltage.

Now, if you try to perturb the Servo Input, the feedback forces the output of the DUT to be almost the same of Servo Input, restoring the same Output voltage.

Note: Voff is the conventional name for input offset voltage, while Vos is the output voltage with Voff applied at the input pins.

An op amp can source or sink current (it can go in or come out).

A good op amp is supposed to have high differential gain (it is supposed to amplify the difference in voltage between the two input terminals).

About your schematic

If you have a positive input voltage on the inverting terminal, the op amp's output will go low quickly. At a certain point, the output voltage of the op amp will be lower than the voltage at the inverting terminal by some amount necessary to make the diode conduct (say, 0.7 V). The diode D2 is now forward-biased because there is a positive input voltage and the output is at a sufficiently lower voltage.

The op amp's output will go to a voltage where the diode conducts the right amount of current (which is also flowing through the input resistor R3) so the appropriate voltage drop occurs across R3 to make the voltage at the inverting terminal 0 V.