How to deal with Daphne bholua suckers?

My Daphne bholua "Jacqueline Postill" shrub has sent up suckers all around for the first time this year. When should I pot them up, and should I remove the rest? The mother plant is ringed with them along the root lines. Also, a couple of branches died during the recent hard winters, and I cut these out. Does this mean the end of my Daphne?

The winter shrub Daphne bholua can be grown from suckers or seeds and sometimes self-sows close to the parent. If well-rooted suckers are produced, you can carefully lift them in winter and pot them up or plant them in good soil. As for removing the rest of the suckers, it depends on whether you want to keep them or not. If you do not want a thicket of Daphne shrubs, then you can remove the suckers. However, if you do want more Daphne shrubs, you can leave them in place or pot them up for later use. A bit of dieback in a Daphne shrub does not mean its demise is imminent, so do not worry about the couple of branches that died during the recent hard winters.