The features of the Beast Titan look, to me, like they resemble Erwin's father. His intensions are completely understandable, considering he knew so much about the titans' history, and was a target for the military police, being killed by them (apparently).
ErwinFather/BeastTitan
Being on the other side of the wall he seems likely to not have the assets to shave his aged hair and beard. I am quite confident about this theory and I'm sure I'm not the only one who believes this.
There have been suggestions contradicting the appearance and comparison between the two.
Mr. Smith has a thin and elongated head with hooked nose, while the Beast Titan has triangular head with a straight nose ~ Manuel de la Fuente
MysteryMan/ErwinFather
- This reference photo looks like the earlier stages of his character design, as we see his beard is not nearly as detailed, so facial features like wrinkles could have also not have been included in the drawing.
It is not only his facial features that are similar... the Beast Titan's illustrations have interesting and uncommon features like the scar on his left arm.
uncanny comparison
The scar on the Beast Titan's left arm is undoubtably a burn mark, but the question is this: how can a Titan Shifter be scarred?
In theory, scars formed before consuming Titan abilities will still stay scarred just as regular scars would.
I think he got the Titan power when he was taken in by the Homeland, and his sadistic attitude just shows how a man can change outside the Walls.
There are claims that Mr. Smith was tortured before being killed, and as we see in the image above, a large candle is being used to burn him; in this angle, whilst the candle wasn't actually touching Mr Smith's left arm, it was in a position just moments away from touching the skin.
If we assume that he was imprisoned and sentenced to death, shortly before somehow escaping, then we can make the connection between this story: there was mention of someone who dug under the walls, and someone else who covered it up and disappeared also. I am confident that it was Mr Smith who escaped.
Special thanks to: Manuel de la Fuente and Jinjehy for additional information