I'm not sure there are any references clearly specifying the ecology of why they are vulnerable, but one can assume from the entries on Immense Mandragora
and that of Mandragora Swarm that's its just something that effects that type of creature. Though with the Immense and Swarm variants, are effected by regular darkness, not the Supernatural Darkness created by Deeper Darkness:
Areas of dim light and darkness become supernaturally dark
I would agree that it would seem logical to stem from them being plants, but as other plants do not have this vulnerablity I would then make the assumption that it has to do with it's ecology and the fact that it is created by the blood or Icor of a Demon, of which demons call home to The Abyss:
Its vast rifts wind throughout the surface of the Outer Sphere, dropping away into bottomless darkness without regard for the realms above which they violate.
If you look up Mandrake, you'll see several referneces to legends that state a Mandrake will scream when it's pulled out of soil (Much as you see in Harry Potter), but it could be connected to that in that they are inert until they are in a lit area.
Nothing I can find points to any specific weakness or vulnerability to darkness in their mythology.