I hope not! George Zimmerman needs to be acquitted. A mistrial means a 2nd trial and a free try for the state.
The defense would not make a motion to dismiss, but a motion for a directed verdict, that would be a not guilty verdict and would stop double jeopardy. However, would not prevent a civil which, BTW, I think is double jeopardy.
If the jury produces a verdict of "Not guilty - self defense", then that should stop anybody from being able to file a civil suit at the state level. However, some imaginative lawyer may be able to figure out a way to file a federal suit on "civil rights" grounds.