It is a coordinate systems problem.
First, What is the coordinate system for your raster before you transform it? (Could you print screen the spatial reference in source tab of layer properties?)
Next i used the Project tool from arc toolbox (Projections and Transformations-Raster) and i create a new shapefile with GreekGrid as spacial reference.
Why did you use Project tool to transform the raster, instead of creating a new shape file with same coordinate of raster? (then transform the result after finishing clip process)
Finally, What is the coordinate system for data frame within all this process?