low voltage clamp circuit (0-200mV)
I'd amplify the input signal so that the new desired clamping levels were 0V and 5V. Then I'd use a rail to rail amplifier running on a 0V and 5V supply. Then I'd attenuate the output by 25 so that 5v became 0.2V and 0V remained at 0V.
If the frequency isn't too high, a simple R2R op-amp should work nicely but the devil's in the detail so maybe a simulation is called for?
Following question amendment I propose this, a precision rectifier: -
It needs to run from split supply rails but will only produce a positive output i.e. it will "clamp" at 0V. Because the circuit is "inverting", a further inverting amplifier will need to be used before this circuit.
I would also consider using a BJT to aid as a voltage follower in order to drive the load. Maybe like this: -
Rload could be as low as a few ohms but the important thing is that the op-amp has the BJT (or MOSFET) inside the closed loop thus maintaining regulation on the output. The output should be capable of supplying a fair bit of current but as you only need 0.2/50 mA it shouldn't be an issue.