Posted: 05/09/2012 at 18:24
You do not say if it is a cultivated blackberry or a wild one.
If you want fruit next year only cut to the ground this years fruiting branches when they have finished fruiting.
If you cut out the non-fruiting shoots you will not get any fruit next year, though you can cut them back a little if they are too long. If you want to propogate new plants pin the end of this year's shoots to the soil and they will root. Then you can sever them from the parent plant.