Let's take a look at some recent players whose draft stock dropped due to off-field concerns:
LeGarrette Blount's stock plummeted after a post-game fight in college. The undrafted rookie ran for over a thousand yards in his first year, and hasn't had an off-field incident in his three years as a pro.
The aforementioned Janoris Jenkins was kicked out of the University of Florida for recurring issues with marijuana - pretty much the same thing that Mathieu was kicked off the LSU football team for. Jenkins started 14 games as a rookie in 2012 and led the league with four defensive touchdowns.
It sounds to me like Mathieu finally understands how to be mature and professional. He's taken all the right steps so far in the pre-draft process. He's already addressed one of the scouts' concerns (speed), though the combine will address some of the others (height and weight).
I would be all over Mathieu in the draft if he starts to drop because of the off-field concerns, and I think that he could be one of the steals of the draft if his stock drops far enough. Keep in mind, he was a Heisman Trophy finalist and won the Chuck Bednarik Award (best defensive player in college football). Several NFL personnel members had called him a first-round talent prior to his dismissal from LSU.
Here's a reminder of what Mathieu used to do during his days as the Honey Badger: