Question: Once you finish the mystery, can you trigger it again?

Get a bizarre fruit from the Curio Shop, go back to the secret lab, and click on the mother and there should be the option to revive her.

From SimsCommunity
Reviving The Mother

Crazy enough to want to do the whole thing over again? After she has been defeated, The Mother can be revived using bizarre fruit. Once you’ve defeated The Mother, all the strange plants growing around StrangerVille will disappear, but the Curio Shop will still have plenty of bizarre fruit in stock. You only need one bizarre fruit to revive The Mother.

With your bizarre fruit in your inventory, select The Mother and choose Revive The Mother. Your Sim will kneel down to give the fruit to her. Some ominous music will play and The Mother will rise from her grave to terrorize StrangerVille once again.

What are the benefits to reviving The Mother? The revived Mother will have some new options available. You can request bizarre fruit from her and communicate with her, but the most interesting interaction is Request Weirdness. Clicking on this will allow you to set the infection level of the town. There is a low, medium, and high option as well as an option for no infection. You can use these options to keep StrangerVille as normal or as weird as you like.

Reviving The Mother also allows you to play through the story again with a different family if you want to. This is useful if you want to try and complete the story a different way; the story can be completed as a civilian or through the military career. You can also give the Hero of StrangerVille trait to another Sim by completing the story again.