Why doesn't the microwave motion sensor make its output negative when the object go away from it?
The module you are using mixes the received reflection with the transmitted signal.
The output is the difference of the two frequencies.
An object moving towards the sensor will cause the reflected signal to have a slightly higher frequency than the transmitted signal.
An object moving away from the sensor will cause the reflected signal to have a slightly lower frequency than the transmitted signal.
If you move towards it at a speed will cause the reflected signal to be 1Hz frequency higher than the reflected signal then the output will be a 1Hz signal.
If you move away from the sensor at the same speed then you would expect the the output to be -1 Hz, but you can't really measure a negative frequency.  The negative just means the signal is inverted - that is, it has been turned on its head.  An inverted sine wave looks just like a non-inverted sine wave.  The only difference is the phase, but you can't measure phase using that module.  To measure phase, you have to have something to mark the starting point.  Your module only has the mixed output, but nothing that could serve as a reference for a phase measurement.
That module is a motion detector that can tell you the speed of the motion but not the velocity.

To detect direction, you would need either a sensor that mixes the received signal with a higher frequency than the transmit signal, or you would need a module with an I and Q output.
If the module were to mix the received signal with a higher frequency than the transmit frequency, then you would have a difference at all times.  With no motion, you would have a fixed frequency output.  With motion, you would have a higher frequency output for an object coming nearer and a lower frequency for an object going away.
I don't think anyone makes a sensor that way.
The IQ option would be simpler.
You have an oscillator at the transmit frequency and a delay circuit that is exactly 90 degrees for your transmit frequency.
You mix the received signal with both the transmit signal and the delayed signal - you get two outputs.
Because of the delay, you have phase information in the two outputs.  With appropriate math, you can figure out if the target is getting closer or further from your sensor.
IQ microwave sensors are a thing.  This company makes some, and I expect others do as well.  That's just the first one I found.