Using Photoshop or Illustrator, what would be the easiest way to recreate the geometric mosaic effect seen below on an image? I realize the image below was likely hand drawn and recreating it in an automated fashion would yield different results but I'm just looking for the tools that may exist to recreate something similar.
What you are looking for is called low-poly or low-polygon art.
A simple search yields many results but bear in mind that NONE will be as good as manually creating the effect.
Here are some options
I'm not sure if there is a program that will automate a flat image to look like a 3D wireframe.
Ovaryraptor's answer is good but it is covering low poly art.
This looks like wireframe to me which is similar but different and does not apply to this question.
You basically need to imagine what it would look like as a 3D low polygon count object and draw where you think the lines would go. This helps if you have a little understanding of what 3D objects look like in wireframe mode.
Here is something someone 3D printed. That might help give you a better idea of what a wireframe of a 3D object might look like. I also thought it was fitting that it had part of the object on the left filled in. That is kind of like the effect of the image you provided.
Here is a picture from the possible duplicate. Which the answer was to use 3D software. But for your purposes its probably just be faster to guess what it would like like and draw the lines manually than it would be to recreate flat art in a 3D program then produce wireframe later.