Why are there two diodes in series in this test circuit?
The circuit includes two diodes to set the negative bias at the base during the turn-off phase of the measurement.

A single diode would only give about 0.7v reverse, two give twice that.

If they didn't have any diodes at all the voltage would exceed the reverse breakdown of the base-emitter junction that is in the region of 7v with silicon planar transistors.

I agree that it is somewhat unusual way to do the test rather than defining the voltage from the pulse generator.