Wishful thinking I'm afraid.
Does he need to ditch the likes of Mandelson etc - yes, can he afford to ditch a whole tranch of the centre - no.
If you think it needs to go further you are really thinking that you know better than the electorate who are to the right of you. That once the underbrush is cleared away they will see the obvious reason, self interest and morality in a socialist alternative. This is simply untrue. It wasn't true for Michael Foot on a fairly socialist manifesto in the early eighties and since then trade unionism and socialist culture have been in retreat. We now need a left that can speak to trade unionists, self employed people and all the other niches below the well off middle classes alike. Saying it has to be something well to the left of most of them is telling people they are wrong.
Have a purge of the most neo-liberal and destructive few, but keep other 'enemies' closer and build something through dialogue and compromise, which to be fair has probably been Corbyn's preference (party man that he is) all along.