Voltage limiter with LM358
The circuit you show is a non-inverting amplifier with a gain of + (1 + 1.2K/9.1K) = 1.132, so you would expect it to output about 1064mV with 940mV in. 

If you want it to output 1000mV with 940mV in then you need to reduce the gain by changing the resistor ratio. For example, you could increase the 9.1K resistor to about 18.8K which would give about 1000mV out for 940mV in. 

On the other hand, if you wish the output to increase linearly and stop at 1000mV as the input voltage increases, then you really do need a limiting circuit. This is independent of the gain requirement- IOW it does not determine the slope or zero intercept of the output voltage, rather it determines where it changes direction and becomes flat with increasing input voltage. 

The easiest way to do that is with something like this: 







simulate this circuit &ndash; Schematic created using CircuitLab

For output voltages from the left amplifier that are less than V1 (1000mV),  the middle amplifier is railed at the positive supply, so D1 is reverse-biased. When the output of the left amplifier exceeds 1000mV, the middle amplifier maintains a voltage of 1000mV at its inverting input by sinking current through D1 and  R1. The right amplifier simply acts as a unit-gain buffer since the output impedance of the limiter is relatively high.