How to mirror a large component in Eagle
The EAGLE mirror command mirrors a part on its origin (or selection on its center) and moves it to the other side of the board. If the origin is not in the center the mirror will result in X or Y translation, which is causing it to go out of bounds for you. 

Edit the part and move its origin to its center. Then any mirroring will not result in X or Y translation. 

Addition:

To edit the part origin open the library which contains the part. Select the package editor (it's the icon with the single logic gate) and select the package of the part you wish to edit. When open, select everything, and move the layout to be centered around the origin mark in the editor screen. Save. Remember to update your libraries in your PCB layout window. The part will now mirror around its center.