I can honestly say that nothing good is not over.
Yes, there are several ways to do this without cutting the image, but I don't even want to describe them - it is long and unreliable.
if the Builder had located at least on the left...
...and if You want to make the drop-down menu, again there will be problems.
remove the negative margin, let the logo climbs on the menu. the design of this will only get better