No, it’s not because it is mirrored, it’s just bad UV unwrapping. You can unwrap with a mirror modifier and it’s not a problem.
It’s better if you apply your mirror modifier though or the symmetry will be too obvious. After you have applied the mirror, be sure your object scale is 1, 1, 1, if not then apply your scale with Control + A. Also check for flipped normals, if there are recalculate with Shift + N.
After that you need to start cutting seams into your model and start unwrapping, but the process is too much to explain via text. Maybe you can watch the Unwrapping of PotHead, that will surely help you out at understanding the process since it holds similarities to your character.
https://cgcookie.com/lessons/unwrapping-the-pot
