This photo was most likely created digitally.
Take a look at how far the mouse's black rump is blurred. It goes all the way back to "at least" the cat's left paw. That means that the exposure time would have had to be at least that long.
Now notice how In focus the mouse's head and the cat's head are. You can practically count the whiskers on the cat.
There are three ways to get images of things moving fast, you can move the camera very carefully at the same speed of the subject, which will create a focused subject with a blurred background or, you can hold the camera still, which will create a blurred subject and a clear background.
The third way is to use a very fast shutter speed which will create a clear subject AND background.
There is no way that I am aware of to create "selective" blurring of both the subject AND the background.
I suspect very careful use of a "smudge tool" that created this image.
I hope the mouse got away, if it was ever even really there to began with.