The new growth you see at the base are 'pups' - new plants. Whether you cut the old growth is entirely up to you. What looks better to you? Let the pups grow on a bit and you can divide them or just leave them be.

You can take new cutting from the mother plant too. Let the cutting dry out a few days then plant it. It will sprout new roots in a couple months. Failure to flower could be insufficient light. Try giving it more light - full on sun if possible.

Watch this video:

https://www.youtube.com/watch?v=Xe-oi626Tko

Barbara, I think I would leave on the old growth till late winter, it would protect the new through the worst of the weather. I'm assuming it is one of our usual euphorbias grown here in the uk...

I also agree about leaving the old stems until after winter. remember when you do cut them that the sap is an irritant so wear gloves.

thanks all. Will wait until spring and hope for flowers.