From looking as closely as I can at the supplied image it looks like it is back focusing a little bit. the blades of grass a bit behind the deer look sharper to me. Were you shooting off of a tripod? If not I would start there and manually focus in magnified live view for the best results since the viewfinder doesn't' have any focusing aids.
I would suggest going to park that has a baseball diamond and go stand out in the outfield on a sunny day with the lens on a big tripod. The do the fine focus adjustment for the lens on the fence behind home plate. That makes a great target and you will be fairly far back. Also keep in mind that wide open 560mm even at a bit of distance it has a fairly narrow depth of field. Stopping it down some will help and the farther away and more stopped down you are the better chance of getting that perfect focus but you will need a lot of light, sitll target or a quality eating high ISO.
If I use
500mm f/5.6 and a distance to subject of 100 feet the DoF is under 3 feet so being at 560mm it would be slightly narrower. So it would be easy to miss the focus by a bit.