"Select color range", select the white area and set fuzziness all the way up. You could hit delete and get this:
and then draw in the white and black behind him how you want it, which would have a cleaner look if you got the patience and steady hand. But also you can use the wand tool and hold Alt to select(technically you're subtracting it form the selection) everything is his face. Then, still with your selection selected, use your lasso tool to select (again you're actually subtracting form the selection) the white part of his tail. Hit backspace or delete then save as PNG. This is what you get:
Note: I didn't erase the white outline but a great way to get rid of it is trace the logo with the pen tool and turn it into a selection, invert selection and delete. Then to get the black outline you can just add a stroke to the layer. If that's too much for you, I'll do it for a couple bucks ha. Hope this helped.
Edit: Was typing this up and doing it in PS while all the responses were being posted haha.